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 A305866 a(n) is the number of primes that are equal to prime(n)+q+1, where prime(n) is the n-th prime number, q is a prime less than or equal to prime(n). 1
 1, 1, 1, 2, 3, 2, 3, 3, 6, 6, 3, 4, 8, 4, 7, 9, 11, 5, 6, 9, 4, 7, 13, 15, 8, 11, 7, 13, 10, 13, 9, 16, 15, 12, 19, 9, 8, 8, 20, 20, 25, 11, 17, 11, 18, 15, 9, 13, 21, 14, 25, 28, 11, 27, 24, 26, 32, 13, 12, 22, 14, 29, 19, 27, 14, 26, 14, 14, 29, 24, 26, 40 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Lei Zhou, Table of n, a(n) for n = 1..10000 EXAMPLE For n=1, p(n)=2, 2+2+1=5 is prime. So a(1)=1; For n=2, p(n)=3, 3+2+1=6 is not prime, 3+3+1=7 is prime. So a(2)=1; ... For n=5, p(5)=11, 11+5+1=17, 11+7+1=19, 11+11+1=23. Three primes found. So a(5)=3. MATHEMATICA Table[ct = 0; p = Prime[i]; Do[q = Prime[j]; If[PrimeQ[p + q + 1], ct++], {j, 1, i}]; ct, {i, 1, 72}] PROG (PARI) a(n) = sum(k=1, n, isprime(prime(n) + prime(k)+1)); \\ Michel Marcus, Jun 12 2018 CROSSREFS Cf. A000040. Sequence in context: A032154 A300651 A003051 * A328406 A257396 A293519 Adjacent sequences:  A305863 A305864 A305865 * A305867 A305868 A305869 KEYWORD nonn,easy AUTHOR Lei Zhou, Jun 12 2018 STATUS approved

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Last modified June 13 20:25 EDT 2021. Contains 345009 sequences. (Running on oeis4.)