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 A377727 #44 Jan 06 2025 15:13:54 %S A377727 0,0,0,0,0,0,0,0,0,3,32,9,207 %N A377727 Number of digit patterns of length n that satisfy no divisibility rules but do not generate primes. %C A377727 Digit patterns (or digital types) are as per A266946. %C A377727 The divisibility rules are per A376918 and they act to exclude patterns which always result in composite numbers, just due to the pattern. %C A377727 There are A376918(n) remaining patterns but not all of them actually contain primes, and a(n) is how many of them do not, so that a(n) = A376918(n) - A267013(n). %C A377727 We call these digital types primonumerophobic and a(n) is the number of these of length n. %C A377727 It is conjectured that the next terms are a(14)=362, a(15)=363, a(16)=1448. This is based on the calculated number of primonumerophobic digit patterns with only 2 or 3 distinct digits and the vanishingly small combinatorial probability for the existence of additional primonumerophobic digit patterns of this length with 4 or more distinct digits. %H A377727 Dmytro S. Inosov and Emil Vlasák, <a href="https://arxiv.org/abs/2410.21427">Cryptarithmically unique terms in integer sequences</a>, arXiv:2410.21427 [math.NT], 2024. %F A377727 a(n) = A376918(n) - A267013(n). %e A377727 For n=10, the a(10) = 3 primonumerophobic patterns of length 10, which are also the smallest which exist, are %e A377727 pattern A266946 %e A377727 ---------- ---------- %e A377727 AAABBBAAAB 1110001110 %e A377727 AABABBBBBA 1101000001 %e A377727 ABAAAAABBB 1011111000 %e A377727 These patterns have 2 distinct digits (A and B) so that there are in total 81 numbers of each pattern that all happen to be composite despite the pattern coefficients in each having no common divisors. %Y A377727 Cf. A267013, A376918, A164864, A266991 %K A377727 nonn,base,more %O A377727 1,10 %A A377727 _Dmytro Inosov_, Nov 05 2024 %E A377727 a(13) = 207 confirmed by _Dmytro Inosov_, Dec 23 2024