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A343764
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a(n) is the number of primes p <= prime(n) such that A007504(n) mod p is prime.
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1
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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
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OFFSET
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1,4
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LINKS
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EXAMPLE
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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.
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MAPLE
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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]);
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PROG
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(PARI) a(n) = my(v=primes(n), s=vecsum(v)); sum(k=1, #v, isprime(s % v[k])); \\ Michel Marcus, Apr 28 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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