A276476 a(n) is the number of distinct integers of the form x^2-x-prime(n) for 0<=x<=prime(n)+1 whose absolute value is prime.

1, 2, 3, 5, 6, 9, 9, 13, 11, 17, 20, 17, 10, 32, 16, 23, 26, 30, 25, 21, 55, 38, 30, 27, 25, 34, 57, 19, 83, 49, 44, 40, 39, 60, 37, 77, 54, 57, 27, 43, 79, 67, 45, 110, 42, 93, 79, 79, 43, 85, 46, 90, 96, 41, 54, 96, 127, 107, 63, 78, 181, 67, 78, 72, 189, 51, 77, 103

Offset

1,2

Links

Table of n, a(n) for n=1..68.

Example

a(2)=2 because prime(2)=3 and x^2 - x - 3 generates {-3, -3, -1, 3, 9}. This contains two integers, -3 and 3, whose absolute value is prime.
a(14)=32 because prime(14)=43 and x^2 - x - 43 generates 32 prime numbers for x = 0..44.

Prog

(PARI) isaprime(x) = isprime(x) || isprime(-x);
nbp(n) = {v = vector(prime(n)+2, x, x--; x^2-x-prime(n)); vp = select(x->isaprime(x), v); vp = Set(vp); #vp; } \\ Michel Marcus, Sep 13 2016

Crossrefs

Cf. A014556, A253827.

Sequence in context: A053784 A036697 A131292 * A069880 A230044 A329269

Adjacent sequences: A276473 A276474 A276475 * A276477 A276478 A276479

Keyword

nonn

Author

Charles Kusniec, Sep 12 2016

Extensions

More terms from Michel Marcus, Sep 13 2016

Status

approved