A155714 Least number expressible as a^2 + p b^2 with positive integers a,b, for each prime p <= prime(n) = A000040(n).

3, 12, 36, 144, 144, 4356, 4356, 4356, 7056, 17424, 176400, 2547216, 2547216, 6290064, 6780816, 6780816, 6780816, 6780816, 93315600, 93315600, 271986064, 271986064, 271986064, 271986064, 271986064, 308213136, 308213136, 308213136

Offset: 1

Author

M. F. Hasler, Feb 10 2009

Keywords

• nonn

Comments

a(n) > 10^9 for n >= 33. [From Donovan Johnson, Sep 29 2009]

Links

• Donovan Johnson, Table of n, a(n) for n=1..32

Crossrefs

Cf. A155715, A028372, A000404, A154777, A092572, A097268, A154778, A155707-A155716, A155560-A155578.

Programs

PARI

A155714(k,n=1) = { local(p); until( !n++, p=prime(k); until( !p=precprime(p-1), for( b=1, sqrtint((n-1)\p), issquare(n-p*b^2) & next(2)); next(2)); break);n}
t=1; for(k=1,30, print1(t=A155714(k,t),","))

Extensions

a(12)-a(32) and b-file from Donovan Johnson, Sep 29 2009