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 A369246 #19 Jan 23 2024 16:29:20 %S A369246 399,4809,5763,63021,76449,1301673,19204051701,421177029231, %T A369246 908999759928891,39248269334566041,39248273246018313, %U A369246 68437232802099093891,4903038892893242229501 %N A369246 Irregular triangle read by rows, where row n lists in ascending order all numbers k in A046316 for which k' = the n-th Euclid number, where k' stands for the arithmetic derivative, and the Euclid numbers are given by A006862. Rows of length zero are simply omitted, i.e., when A369245(n) = 0. %C A369246 All terms are multiples of 3 because for all n >= 2, A006862(n) = 1 + A002110(n) == +1 (mod 3), see A369252. %C A369246 Although the first thirteen terms appear in the ascending order, this might not be true for all the later terms, if they exist. %e A369246 Rows 1..3 have no terms. %e A369246 Row 4 has one term: 399 = 3 * 7 * 19, whose arithmetic derivative (see A003415) 399' is 211 = 1 + prime(4)# [= A006862(4)]. %e A369246 Row 5 has two terms: 4809 = 3 * 7 * 229 and 5763 = 3 * 17 * 113, with 4809' = 5763' = 2311 = 1 + prime(5)#. %e A369246 Row 6 has two terms: 63021 = 3 * 7 * 3001 and 76449 = 3 * 17 * 1499, with 63021' = 76449' = 30031 = 1 + prime(6)#. %e A369246 Row 7 has one term: 1301673 = 3 * 17 * 25523, whose arithmetic derivative is 510511 = 1 + prime(7)#. %e A369246 Rows 8 and 9 have no terms. %e A369246 Row 10 has one term: 19204051701 = 3 * 281 * 22780607, whose arithmetic derivative is 6469693231 = 1 + prime(10)#. %e A369246 Row 11 has one term: 421177029231 = 3 * 7 * 20056049011, whose arithmetic derivative is 200560490131 = 1 + prime(11)#. %e A369246 Row 12 has no terms. %e A369246 Row 13 has one term: 908999759928891 = 3 * 727 * 416781182911, whose arithmetic derivative is 304250263527211 = 1 + prime(13)#. %e A369246 Row 14 has two terms: 39248269334566041 = 3 * 8071457 * 1620866771, and 39248273246018313 = 3 * 11056387 * 1183276033, which both have arithmetic derivative 13082761331670031 = 1 + prime(14)#. %e A369246 Row 15 has no terms. %e A369246 Row 16 has one term: 68437232802099093891 = 3 * 7 * 3258915847719004471, whose arithmetic derivative is 32589158477190044731 = 1 + prime(16)#. %e A369246 Row 17 has at least this term: 4903038892893242229501 = 3 * 17 * 96138017507710631951, whose arithmetic derivative is 1922760350154212639071 = 1 + prime(17)#. %Y A369246 Subsequence of A008585 and of A046316. %Y A369246 Cf. A003415, A002110, A006862, A369054, A369245 (counts of solutions, length of row n), A369252. %Y A369246 Cf. also A366890, A369240 for similar tables. %K A369246 nonn,tabf,hard,more %O A369246 1,1 %A A369246 _Antti Karttunen_, Jan 22 2024