A278500 a(n) = largest k such that n+1 = a prime, n+2 = 2 * a prime, ..., n+k is k times a prime, a(n) = 0 if n+1 is not a prime.

1, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 3, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,2

Comments

First 4 occurs at n=12720, first 5 occurs at n=19440. See A074200.

Links

Antti Karttunen, Table of n, a(n) for n = 1..21000

Example

a(12) = 3 as 13 = 1*prime, 14 = 2*prime, 15 = 3*prime.

Mathematica

Table[If[CompositeQ[n + 1], 0, k = 1; While[Times @@ Boole@ Map[PrimeQ, MapIndexed[#1/First@ #2 &, (n + Range@ k)]] == 1, k++]; k - 1], {n, 120}] (* Michael De Vlieger, Dec 01 2016 *)

Prog

(PARI)
A278500(n) = { my(k=1); while((!((n+k)%k) && isprime((n+k)/k)), k = k+1); (k-1); }
for(n=1, 2^20, write("b278500.txt", n, " ", A278500(n)));
(Scheme) (define (A278500 n) (let loop ((k 1)) (let ((h (/ (+ n k) k))) (if (or (not (integer? h)) (zero? (A010051 h))) (- k 1) (loop (+ 1 k))))))

Crossrefs

Cf. A072668 (positions of zeros), A006093 (nonzeros), A089965 (positions of terms >= 2), A278583 (of terms >= 3), A278585 (of terms >= 4).

Cf. A074200 (position of the first term >= n).

Sequence in context: A283978 A002655 A064891 * A035211 A352558 A324735

Adjacent sequences: A278497 A278498 A278499 * A278501 A278502 A278503

Keyword

nonn

Author

Antti Karttunen, Nov 30 2016

Status

approved