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

1,1

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

Prog

(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), ", "))

Crossrefs

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

Sequence in context: A247008 A344062 A303308 * A282022 A004661 A074430

Adjacent sequences: A155711 A155712 A155713 * A155715 A155716 A155717

Keyword

nonn

Author

M. F. Hasler, Feb 10 2009

Extensions

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

Status

approved