Originally Posted by OppsIdidItAgain View Post
my user-numeral, and its reciprocal, from the gematria forums, 7152.
The sequence of positive integers N, such that the first digit of N^N is "7" is

56, 69, 90, 95, 102, 139, 154, 165, 168, 174, 177, 222, 242, 260, 267, 283, 292, 303, 316, 335, 336, 401, 402, 422, 437, 449, 460, 470, 479, 503, 510, 517, 530, 548, 570, 600, 627, 648, 652, 656, 660, 701, 722, 755, 774, 777, 807, 810, 833, 866, 874, 895, 918, 923, 928, 933, 974, 1002, 1018, 1027, 1047, 1088, 1107, 1138, 1140, 1142, 1184, 1186, 1188, 1190, 1221, 1242, 1257, 1283, 1305, 1341, 1364, 1371, 1378, 1433, 1438, 1493, 1511, 1524, 1545, 1553, 1561, 1580, 1591, 1602, 1630, 1647, 1650, 1676, 1679, 1736, 1739, 1767, 1786, 1802, 1815, 1828, 1838, 1848, 1858, 1875, 1931, 1938, 1982, 1997, 2012, 2016, 2039, 2043, 2047, 2091, 2095, 2124, 2141, 2158, 2171, 2193, 2202, 2211, 2234, 2262, 2281, 2286, 2361, 2382, 2398, 2442, 2459, 2482, 2488, 2494, 2500, 2506, 2512, 2518, 2524, 2530, 2555, 2607, 2634, 2641, 2648, 2655, 2684, 2691, 2706, 2721, 2729, 2793, 2810, 2827, 2836, 2845, 2854, 2863, 2891, 2901, 2951, 2972, 2983, 2994, 3017, 3029, 3041, 3053, 3078, 3091, 3105, 3147, 3162, 3194, 3210, 3227, 3245, 3264, 3284, 3305, 3327, 3350, 3351, 3376, 3377, 3404, 3405, 3436, 3437, 3472, 3473, 3517, 3518, 3519, 3580, 3581, 3582, 3583, 3584, 3774, 3775, 3776, 3777, 3778, 3841, 3842, 3843, 3888, 3889, 3926, 3927, 3960, 3989, 3990, 4017, 4042, 4066, 4088, 4089, 4110, 4130, 4149, 4150, 4168, 4186, 4204, 4221, 4237, 4269, 4299, 4314, 4328, 4342, 4356, 4383, 4396, 4409, 4421, 4434, 4446, 4458, 4470, 4482, 4493, 4505, 4516, 4527, 4538, 4549, 4560, 4581, 4602, 4612, 4642, 4652, 4662, 4681, 4700, 4719, 4728, 4737, 4746, 4755, 4764, 4773, 4782, 4808, 4825, 4842, 4850, 4867, 4875, 4883, 4923, 4931, 4939, 4962, 4970, 4985, 5000, 5015, 5030, 5052, 5059, 5095, 5102, 5109, 5116, 5123, 5130, 5164, 5171, 5191, 5211, 5224, 5263, 5276, 5295, 5314, 5320, 5345, 5351, 5447, 5453, 5459, 5482, 5505, 5522, 5539, 5556, 5567, 5578, 5589, 5600, 5611, 5622, 5649, 5665, 5681, 5702, 5723, 5749, 5754, 5795, 5800, 5805, 5810, 5815, 5820, 5825, 5830, 5835, 5840, 5845, 5850, 5855, 5860, 5865, 5904, 5909, 5938, 5962, 5981, 5995, 6014, 6028, 6042, 6065, 6088, 6097, 6178, 6187, 6209, 6231, 6244, 6257, 6270, 6283, 6300, 6313, 6330, 6347, 6351, 6368, 6372, 6393, 6418, 6422, 6455, 6459, 6516, 6520, 6524, 6528, 6532, 6536, 6540, 6544, 6548, 6552, 6556, 6560, 6564, 6568, 6623, 6627, 6631, 6662, 6666, 6693, 6716, 6735, 6754, 6773, 6788, 6803, 6818, 6833, 6844, 6870, 6881, 6892, 6903, 6914, 6943, 6954, 6972, 6990, 6997, 7015, 7022, 7047, 7054, 7145, 7152, ...

7152 is the 417th entry of this sequence. This sequence is not attested in the OEIS, though I suppose you could submit it for inclusion. When considering the first digit of N^N, the digits "1" and "3" are vastly over represented.

"vastly over represented" = "deterrent spray evolves"