Hexadecimal Words

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.

Figure 1: permalink
On vertical scale 1.0 = One Million