A263770 - OEIS

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A263770

Smallest prime q such that (prime(n)^2 + q*prime(n))/(prime(n) + 1) is an integer.

2

7, 5, 7, 17, 13, 29, 19, 41, 73, 31, 97, 191, 43, 89, 97, 109, 61, 311, 137, 73, 149, 241, 337, 181, 197, 103, 313, 109, 331, 229, 257, 397, 139, 281, 151, 457, 317, 821, 337, 349, 181, 547, 193, 389, 199, 401, 1061, 449, 229, 461, 937, 241, 727, 757, 1033, 1321, 271, 1361, 557

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OFFSET

1,1

COMMENTS

Least prime q such that q == 1 (mod prime(n) + 1).

Consists of the initial terms of sequences A002476, A002144, A002476, A007519, A068228, A140444, A061237, A141881, A107008, A132230, A133870, A141868, A124826, A142292, A142398, A141948, A088955, A142003, ...

LINKS

Table of n, a(n) for n=1..59.

FORMULA

5 is in this sequence because (prime(2)^2 + 5*prime(2))/(prime(2) + 1) = 6 and 5 is prime.

MATHEMATICA

Table[q = 2; While[! IntegerQ[(Prime[n]^2 + q Prime@ n)/(Prime@ n + 1)], q = NextPrime@ q]; q, {n, 59}] (* Michael De Vlieger, Oct 26 2015 *)

PROG

(PARI) a(n) = {p = prime(n); q = 2; while ((p^2 + p*q) % (p + 1), q = nextprime(q+1)); q; } \\ Michel Marcus, Oct 26 2015

CROSSREFS

Cf. A263729, A263730, A263769.

Sequence in context: A143297 A195348 A072449 * A088839 A111769 A111513

Adjacent sequences: A263767 A263768 A263769 * A263771 A263772 A263773

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Oct 25 2015

STATUS

approved