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

%I #6 Jul 14 2012 11:32:23

%S 3,12,36,144,144,4356,4356,4356,7056,17424,176400,2547216,2547216,

%T 6290064,6780816,6780816,6780816,6780816,93315600,93315600,271986064,

%U 271986064,271986064,271986064,271986064,308213136,308213136,308213136

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

%C a(n) > 10^9 for n >= 33. [From _Donovan Johnson_, Sep 29 2009]

%H Donovan Johnson, <a href="/A155714/b155714.txt">Table of n, a(n) for n=1..32</a>

%o (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}

%o t=1; for(k=1,30, print1(t=A155714(k,t),","))

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

%K nonn

%O 1,1

%A _M. F. Hasler_, Feb 10 2009

%E a(12)-a(32) and b-file from _Donovan Johnson_, Sep 29 2009