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 A321392 #15 Nov 12 2018 15:20:44 %S A321392 1,1,2,1,2,3,4,4,3,5,6,7,7,7,7,10,11,10,12,11,11,12,11,13,16,14,13,10, %T A321392 14,13,21,19,19,17,20,21,24,26,25,25,25,23,26,26,24,26,29,33,27,30,31, %U A321392 28,32,33,32,34,34,34,32,31,34,37,37,41,36,38,41,44,45 %N A321392 a(n) is the number of bases b > 1 such that prime(n) + digitsum(prime(n), base b) is prime (where prime(n) denotes the n-th prime number). %C A321392 For any prime number p and base b > p, p + digitsum(p, base b) equals twice p and is not prime, hence the sequence is well defined. %C A321392 For prime(n) + digitsum(prime(n), base b) to be prime, b must be even (see A320866). %H A321392 Rémy Sigrist, <a href="/A321392/b321392.txt">Table of n, a(n) for n = 1..10000</a> %H A321392 Rémy Sigrist, <a href="/A321392/a321392.png">Colored scatterplot of (n, b) such that prime(n) + sumdigits(prime(n), base 2*b) is prime and 1 <= n <= 2000 and 1 <= b <= 1000</a> (where the color is function of floor(prime(n) / (2*b))) %F A321392 a(n) = A321393(A000040(n)). %e A321392 For n = 6, we have prime(6) = 13 and: %e A321392 b 13 + sumdigits(13, base b) %e A321392 ---- -------------------------- %e A321392 2 16 %e A321392 4 17 (prime) %e A321392 6 16 %e A321392 8 19 (prime) %e A321392 10 17 (prime) %e A321392 12 15 %e A321392 >=14 26 %e A321392 Hence, a(6) = 3. %o A321392 (PARI) a(n) = my (p=prime(n)); sum(b=1, p\2, isprime(p+sumdigits(p, 2*b))) %Y A321392 Cf. A000040, A243441, A320866, A321393. %K A321392 nonn,base %O A321392 1,3 %A A321392 _Rémy Sigrist_, Nov 08 2018