Certain hexadecimal numbers contain only letters between A (10) and F (16) and so can form English words. The commonly accepted words are:
a, aba, abaca, abed, accede, acceded, ace, aced, ad, add, added, baa, baad, babe, bad, bade, baff, baffed, be, bead, beaded, bed, bedded, bee, beef, beefed, cab, cad, cade, cafe, cede, ceded, cee, dab, dabbed, dace, dad, daff, dead, deaf, decade, dee, deed, deeded, deface, defaced, ebb, ebbed, efface, effaced, fa, facade, face, faced, fad, fade, faded, fed, fee, feed
These hexadecimal "words" with their decimal equivalents are shown below (arranged alphabetically):
10 --> a
2746 --> aba
703178 --> abaca
44013 --> abed
11325150 --> accede
181202413 --> acceded
2766 --> ace
44269 --> aced
173 --> ad
2781 --> add
712173 --> added
2986 --> baa
47789 --> baad
47806 --> babe
2989 --> bad
47838 --> bade
47871 --> baff
12255213 --> baffed
190 --> be
48813 --> bead
12496365 --> beaded
3053 --> bed
12508653 --> bedded
3054 --> bee
48879 --> beef
12513261 --> beefed
3243 --> cab
3245 --> cad
51934 --> cade
51966 --> cafe
52958 --> cede
847341 --> ceded
3310 --> cee
3499 --> dab
14334957 --> dabbed
56014 --> dace
3501 --> dad
56063 --> daff
57005 --> dead
57007 --> deaf
14600926 --> decade
3566 --> dee
57069 --> deed
14609901 --> deeded
14613198 --> deface
233811181 --> defaced
3771 --> ebb
965613 --> ebbed
15727310 --> efface
251636973 --> effaced
250 --> fa
16435934 --> facade
64206 --> face
1027309 --> faced
4013 --> fad
64222 --> fade
1027565 --> faded
4077 --> fed
4078 --> fee
65261 --> feed
The decimal numbers in ascending order are:
10, 173, 190, 250, 2746, 2766, 2781, 2986, 2989, 3053, 3054, 3243, 3245, 3310, 3499, 3501, 3566, 3771, 4013, 4077, 4078, 44013, 44269, 47789, 47806, 47838, 47871, 48813, 48879, 51934, 51966, 52958, 56014, 56063, 57005, 57007, 57069, 64206, 64222, 65261, 703178, 712173, 847341, 965613, 1027309, 1027565, 11325150, 12255213, 12496365, 12508653, 12513261, 14334957, 14600926, 14609901, 14613198, 15727310, 16435934, 181202413, 233811181, 251636973
OEIS A132676 shows these same numbers.
If we are only interested in decimal numbers whose hexadecimal equivalents contain only letters and no digits from 0 to 9 then these are listed in OEIS A228774. Up to 40000, there are 258 of them and they can be generated via this permalink.
10, 11, 12, 13, 14, 15, 170, 171, 172, 173, 174, 175, 186, 187, 188, 189, 190, 191, 202, 203, 204, 205, 206, 207, 218, 219, 220, 221, 222, 223, 234, 235, 236, 237, 238, 239, 250, 251, 252, 253, 254, 255, 2730, 2731, 2732, 2733, 2734, 2735, 2746, 2747, 2748, 2749, 2750, 2751, 2762, 2763, 2764, 2765, 2766, 2767, 2778, 2779, 2780, 2781, 2782, 2783, 2794, 2795, 2796, 2797, 2798, 2799, 2810, 2811, 2812, 2813, 2814, 2815, 2986, 2987, 2988, 2989, 2990, 2991, 3002, 3003, 3004, 3005, 3006, 3007, 3018, 3019, 3020, 3021, 3022, 3023, 3034, 3035, 3036, 3037, 3038, 3039, 3050, 3051, 3052, 3053, 3054, 3055, 3066, 3067, 3068, 3069, 3070, 3071, 3242, 3243, 3244, 3245, 3246, 3247, 3258, 3259, 3260, 3261, 3262, 3263, 3274, 3275, 3276, 3277, 3278, 3279, 3290, 3291, 3292, 3293, 3294, 3295, 3306, 3307, 3308, 3309, 3310, 3311, 3322, 3323, 3324, 3325, 3326, 3327, 3498, 3499, 3500, 3501, 3502, 3503, 3514, 3515, 3516, 3517, 3518, 3519, 3530, 3531, 3532, 3533, 3534, 3535, 3546, 3547, 3548, 3549, 3550, 3551, 3562, 3563, 3564, 3565, 3566, 3567, 3578, 3579, 3580, 3581, 3582, 3583, 3754, 3755, 3756, 3757, 3758, 3759, 3770, 3771, 3772, 3773, 3774, 3775, 3786, 3787, 3788, 3789, 3790, 3791, 3802, 3803, 3804, 3805, 3806, 3807, 3818, 3819, 3820, 3821, 3822, 3823, 3834, 3835, 3836, 3837, 3838, 3839, 4010, 4011, 4012, 4013, 4014, 4015, 4026, 4027, 4028, 4029, 4030, 4031, 4042, 4043, 4044, 4045, 4046, 4047, 4058, 4059, 4060, 4061, 4062, 4063, 4074, 4075, 4076, 4077, 4078, 4079, 4090, 4091, 4092, 4093, 4094, 4095
The final number (4095) in the list above is equivalent to "f f f" in hexadecimal. All the English words listed at the start of this post will be included in this list of course. Up to one million, there are 8034 such decimal numbers with letter-only hexadecimal equivalents and there are significant gaps between groups of numbers. See Figure 1.
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Figure 1: permalink On vertical scale 1.0 = One Million |
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