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 A321393 #17 Nov 12 2018 03:55:07 %S A321393 1,1,2,2,1,1,1,3,2,2,2,3,4,4,5,4,2,4,2,3,4,3,2,5,6,5,5,5,4,6,5,5,6,6, %T A321393 6,7,8,7,6,7,5,7,6,5,8,7,5,10,8,6,9,10,6,9,12,8,10,11,8,10,10,8,9,12, %U A321393 7,12,10,9,11,11,9,11,11,10,13,11,9,12,10,9 %N A321393 a(n) is the number of bases b > 1 such that n + digitsum(n, base b) is prime. %C A321393 For any n > 1 and b > n, n + digitsum(n, base b) equals 2*n and is composite, hence the sequence is well defined. %C A321393 The sequence is not defined for n = 1 as 1 + digitsum(1, base b) equals 2 and is prime for any base b > 1. %C A321393 In the scatterplot of the sequence, the points are separated into two beams according to whether n is divisible by 3 or not, then these beams are separated in two according to whether n is divisible by 5 or not, then similarly according to whether n is divisible by 7 or not; these separations seem to continue for each odd prime number; see scatterplot in Links section. %H A321393 Rémy Sigrist, <a href="/A321393/b321393.txt">Table of n, a(n) for n = 2..10000</a> %H A321393 Rémy Sigrist, <a href="/A321393/a321393.png">Colored scatterplot of the sequence for n = 2..250000</a> %H A321393 Rémy Sigrist, <a href="/A321393/a321393_1.png">Colored scatterplot of (n, b) such that n + sumdigits(n, base b) is prime and 1 <= n <= 1000 and 2 <= b <= 1000</a> (where the color is function of n + sumdigits(n, base b)) %e A321393 For n = 9, we have: %e A321393 b 9 + sumdigits(9, base b) %e A321393 ---- ------------------------ %e A321393 2 11 (prime) %e A321393 3 10 %e A321393 4 12 %e A321393 5 14 %e A321393 6 13 (prime) %e A321393 7 12 %e A321393 8 11 (prime) %e A321393 9 10 %e A321393 >=10 18 %e A321393 Hence, a(9) = 3. %o A321393 (PARI) a(n) = sum(b=2, n, isprime(n + sumdigits(n, b))) %Y A321393 Cf. A321392. %K A321393 nonn,base %O A321393 2,3 %A A321393 _Rémy Sigrist_, Nov 08 2018