A343764 a(n) is the number of primes p <= prime(n) such that A007504(n) mod p is prime.

0, 1, 0, 3, 1, 2, 4, 2, 2, 2, 2, 7, 2, 4, 4, 7, 6, 6, 8, 6, 6, 5, 8, 8, 4, 5, 6, 9, 7, 11, 7, 11, 10, 10, 7, 12, 9, 12, 12, 13, 10, 12, 14, 7, 17, 6, 12, 16, 10, 23, 11, 18, 10, 13, 16, 11, 12, 19, 17, 20, 15, 13, 17, 18, 11, 20, 16, 19, 19, 13, 19, 19, 16, 20, 15, 16, 16, 18, 15, 16, 26, 21, 23

Offset

1,4

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(7) = 4 because A097504(7) = 58 and of the first 7 primes p, there are 4 for which 58 mod p is prime, namely 58 mod 5 = 3, 58 mod 7 = 2, 58 mod 31 = 3 and 58 mod 17 = 7.

Maple

P:= [seq(ithprime(i), i=1..100)]:
SP:= ListTools:-PartialSums(P):
f:= proc(n) local t, L;
    t:= SP[n];
    L:= P[1..n];
    nops(select(p -> member(t mod p, L), L))
end proc:
map(f, [$1..100]);

Prog

(PARI) a(n) = my(v=primes(n), s=vecsum(v)); sum(k=1, #v, isprime(s % v[k])); \\ Michel Marcus, Apr 28 2021

Crossrefs

Cf. A097504

Sequence in context: A004608 A366936 A201673 * A117905 A133445 A139457

Adjacent sequences: A343761 A343762 A343763 * A343765 A343766 A343767

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Apr 28 2021

Status

approved