This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367854 #27 Jan 19 2024 21:33:56 %S A367854 1,2,4,6,72,75,152,518,631,1585,2512,4217,5275,13895,14678,53367, %T A367854 177828,464159,1154782,2154435,3162278,4641589,8483429,8576959, %U A367854 13894955,15848932,21544347,68129207,74989421,100000001,114504757,170125428,517947468,1000000001 %N A367854 Indices at which record high values occur in A367821. %C A367854 Each term after a(1) = 1 is the smallest integer whose base-10 logarithm exceeds some ratio of integers N/D with D <= 21 = floor(1/(1 - log_10(9))); see Example section. - _Jon E. Schoenfield_, Dec 03 2023 %e A367854 From _Jon E. Schoenfield_, Dec 03 2023: (Start) %e A367854 The following table illustrates how the base-10 logarithm of each term from a(2) through a(17) is slightly larger than a ratio of integers N/D with D <= 21. %e A367854 . %e A367854 n a(n) log_10(a(n)) N/D log_10(a(n))*D %e A367854 -- ------ -------------- ----- -------------- %e A367854 2 2 0.301029995... 3/10 3.01029995... %e A367854 3 4 0.602059991... 3/5 3.01029995... %e A367854 4 6 0.778151250... 7/9 7.00336125... %e A367854 5 72 1.857332496... 13/7 13.00132747... %e A367854 6 75 1.875061263... 15/8 15.00049010... %e A367854 7 152 2.181843587... 24/11 24.00027946... %e A367854 8 518 2.714329759... 19/7 19.00030831... %e A367854 9 631 2.800029359... 14/5 14.00014679... %e A367854 10 1585 3.200029266... 16/5 16.00014633... %e A367854 11 2512 3.400019635... 17/5 17.00009817... %e A367854 12 4217 3.625003601... 29/8 29.00002880... %e A367854 13 5275 3.722222463... 67/18 67.00000435... %e A367854 14 13895 4.142858551... 29/7 29.00000985... %e A367854 15 14678 4.166666883... 25/6 25.00000130... %e A367854 16 53367 4.727272789... 52/11 52.00000068... %e A367854 17 177828 5.250000144... 21/4 21.00000057... %e A367854 ... %e A367854 E.g., log_10(a(17)) = log_10(177828) slightly exceeds 21/4; 10^(21/4) = 10^5 * 10^(1/4) = 100000 * 1.77827941..., so 177828^k is slightly farther above the nearest lower power of 10 than 177828^(k-4) is. This near-periodic behavior of the mantissas, with their slow upward creep at every 4th exponent, explains why none of the mantissas of 177828^k begin with 9 until k gets very large: %e A367854 . %e A367854 k 177828^k %e A367854 ------- ------------------ %e A367854 1 1.7782800e+0000005 %e A367854 2 3.1622799e+0000010 %e A367854 3 5.6234188e+0000015 %e A367854 4 1.0000013e+0000021 %e A367854 5 1.7782824e+0000026 %e A367854 6 3.1622840e+0000031 %e A367854 7 5.6234263e+0000036 %e A367854 8 1.0000027e+0000042 %e A367854 9 1.7782847e+0000047 %e A367854 10 3.1622882e+0000052 %e A367854 11 5.6234338e+0000057 %e A367854 ... %e A367854 15 5.6234412e+0000078 %e A367854 19 5.6234487e+0000099 %e A367854 23 5.6234562e+0000120 %e A367854 ... %e A367854 1417539 8.9999657e+7442079 %e A367854 1417543 8.9999776e+7442100 %e A367854 1417547 8.9999896e+7442121 %e A367854 1417551 9.0000015e+7442142 %e A367854 (End) %Y A367854 Cf. A367821. %K A367854 nonn,base %O A367854 1,2 %A A367854 _William Hu_, Dec 02 2023 %E A367854 More terms from _Jon E. Schoenfield_, Dec 03 2023