A097143 - OEIS

A097143

a(n) is the least prime greater than a(n-1) such that n is a quadratic residue mod p.

2, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 61, 67, 71, 83, 89, 101, 109, 127, 137, 173, 191, 193, 197, 227, 233, 239, 241, 251, 257, 263, 269, 271, 277, 293, 313, 317, 347, 349, 353, 383, 389, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 463, 479

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OFFSET

1,1

COMMENTS

a(10^n): 2,41,1229,16693,220721,2734801,32393839,..., .

Conjecture: Lim_n->Inf a(n)/A097144(n) = 1 <==> a(P_2n).

LINKS

Table of n, a(n) for n=1..56.

Eric Weisstein's World of Mathematics, Quadratic Residue.

MATHEMATICA

a[1] = 2; a[n_] := a[n] = Block[{k = PrimePi[ a[n - 1]] + 1}, While[ JacobiSymbol[n, Prime[k]] != 1, k++ ]; Prime[k]]; Table[ a[n], {n, 20}]

CROSSREFS