Catch-22 Numbers

On October 4th of 2021, I turned 26482 days old and noted that the sum of its digits is 22. Now 22 is considered a very powerful number in numerology, along with 11 and 33. Not only do the digits of 26482 add to 22 but the number is "framed" by 22:

26482

Digit sum is 22

If the digits of a number contain the digit 2 exactly twice and if the sum of the digits is a multiple of 22, then we might term such numbers Catch-22 numbers. How many of them are there, up to the one million mark? Well, it turns out not that many. There are 6360 such numbers representing 0.636 percent of the total. The minimum is 2299 and the maximum is 992200. Here is a permalink to the SageMathCell calculation.

Catch-22 numbers

First member is 2299

Digit sum is 22

What if the number itself was a multiple of 22? Applying this criterion leads not surprisingly to a significant reduction in the numbers. There are 522 such numbers representing 0.0522 percent of all the numbers up to one million. The minimum is now 2992 and the maximum remains the same (992200). Such numbers might be termed Super Catch-22 numbers. Here is a permalink to the SageMathCell calculation.

First member is 2992

Digit sum is 22

2992 = 22 x 136

Here are the 522 Super Catch-22 numbers in the range up to one million:

[2992, 9922, 12298, 12892, 19228, 19822, 22198, 22396, 22594, 22990, 23782, 24772, 25762, 26752, 27742, 28732, 29128, 29326, 29524, 29920, 32296, 32692, 39226, 39622, 42592, 49522, 52294, 52492, 59224, 59422, 62392, 69322, 73282, 74272, 75262, 76252, 77242, 78232, 82192, 89122, 92092, 92290, 99022, 99220, 102982, 108922, 112288, 112882, 118228, 118822, 121792, 122188, 122386, 122584, 122980, 123772, 124762, 125752, 126742, 127732, 128128, 128326, 128524, 128920, 129712, 132286, 132682, 138226, 138622, 142582, 148522, 152284, 152482, 158224, 158422, 162382, 168322, 171292, 173272, 174262, 175252, 176242, 177232, 179212, 182182, 188122, 192082, 192280, 198022, 198220, 200992, 201982, 202378, 202576, 202774, 203962, 204952, 205942, 206932, 207328, 207526, 207724, 208912, 209902, 210298, 210892, 211288, 211882, 212476, 212674, 213268, 213862, 214258, 214852, 215248, 215842, 216238, 216832, 217426, 217624, 218218, 218812, 219208, 219802, 220198, 220396, 220594, 220990, 221188, 221386, 221584, 221980, 223168, 223366, 223564, 223960, 224158, 224356, 224554, 224950, 225148, 225346, 225544, 225940, 226138, 226336, 226534, 226930, 228118, 228316, 228514, 228910, 229108, 229306, 229504, 229900, 230296, 230692, 231286, 231682, 232078, 232474, 232870, 233266, 233662, 234256, 234652, 235246, 235642, 236236, 236632, 237028, 237424, 237820, 238216, 238612, 239206, 239602, 240592, 241582, 242176, 242374, 242770, 243562, 244552, 245542, 246532, 247126, 247324, 247720, 248512, 249502, 250294, 250492, 251284, 251482, 252076, 252670, 253264, 253462, 254254, 254452, 255244, 255442, 256234, 256432, 257026, 257620, 258214, 258412, 259204, 259402, 260392, 261382, 262174, 262570, 263362, 264352, 265342, 266332, 267124, 267520, 268312, 269302, 272074, 272470, 277024, 277420, 280192, 281182, 282370, 283162, 284152, 285142, 286132, 287320, 288112, 289102, 290092, 290290, 291082, 291280, 293062, 293260, 294052, 294250, 295042, 295240, 296032, 296230, 298012, 298210, 299002, 299200, 302962, 306922, 312268, 312862, 316228, 316822, 320782, 321772, 322168, 322366, 322564, 322960, 323752, 324742, 325732, 326128, 326326, 326524, 326920, 327712, 328702, 332266, 332662, 336226, 336622, 342562, 346522, 352264, 352462, 356224, 356422, 362362, 366322, 370282, 371272, 373252, 374242, 375232, 377212, 378202, 382162, 386122, 392062, 392260, 396022, 396220, 402952, 405922, 412258, 412852, 415228, 415822, 420772, 421762, 422158, 422356, 422554, 422950, 423742, 424732, 425128, 425326, 425524, 425920, 426712, 427702, 432256, 432652, 435226, 435622, 442552, 445522, 452254, 452452, 455224, 455422, 462352, 465322, 470272, 471262, 473242, 474232, 476212, 477202, 482152, 485122, 492052, 492250, 495022, 495220, 502942, 504922, 512248, 512842, 514228, 514822, 520762, 521752, 522148, 522346, 522544, 522940, 523732, 524128, 524326, 524524, 524920, 525712, 526702, 532246, 532642, 534226, 534622, 542542, 544522, 552244, 552442, 554224, 554422, 562342, 564322, 570262, 571252, 573232, 575212, 576202, 582142, 584122, 592042, 592240, 594022, 594220, 602932, 603922, 612238, 612832, 613228, 613822, 620752, 621742, 622138, 622336, 622534, 622930, 623128, 623326, 623524, 623920, 624712, 625702, 632236, 632632, 633226, 633622, 642532, 643522, 652234, 652432, 653224, 653422, 662332, 663322, 670252, 671242, 674212, 675202, 682132, 683122, 692032, 692230, 693022, 693220, 702328, 702526, 702724, 712426, 712624, 720742, 721732, 723712, 724702, 732028, 732424, 732820, 742126, 742324, 742720, 752026, 752620, 762124, 762520, 770242, 771232, 772024, 772420, 773212, 774202, 782320, 801922, 802912, 811228, 811822, 812218, 812812, 820732, 821128, 821326, 821524, 821920, 822118, 822316, 822514, 822910, 823702, 831226, 831622, 832216, 832612, 841522, 842512, 851224, 851422, 852214, 852412, 861322, 862312, 870232, 873202, 881122, 882112, 891022, 891220, 892012, 892210, 900922, 902902, 910228, 910822, 912208, 912802, 920128, 920326, 920524, 920920, 921712, 922108, 922306, 922504, 922900, 930226, 930622, 932206, 932602, 940522, 942502, 950224, 950422, 952204, 952402, 960322, 962302, 971212, 980122, 982102, 990022, 990220, 992002, 992200]