_M. F. Hasler (www.univ-ag.fr/~mhasler), _, Jan 27 2009

a(n) > 10^9 for n >= 47. [From _Donovan Johnson (donovan.johnson(AT)yahoo.com), _, Sep 29 2009]

a(23)-a(46) and b-file from _Donovan Johnson (donovan.johnson(AT)yahoo.com), _, Sep 29 2009

Donovan Johnson, <a href="/A155715/b155715.txt">Table of n, a(n) for n=1..46</a>

nonn,new

nonn

nonn,new

nonn

M. F. Hasler (MHasler(AT)www.univ-ag.fr/~mhasler), Jan 27 2009

2, 17, 73, 73, 241, 241, 1009, 1009, 1009, 1009, 7561, 7561, 21961, 32356, 32356, 32356, 44641, 44641, 349924, 349924, 349924, 349924, 1399696, 1399696, 1399696, 3027249, 3027249, 3027249, 4349601, 4349601, 18567396, 18567396, 18567396

a(n) > 10^9 for n >= 47. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 29 2009]

Donovan Johnson, <a href="b155715.txt">Table of n, a(n) for n=1..46</a>

more,nonn,new

nonn

a(23)-a(46) and b-file from Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 29 2009

Least number expressible as a^2 + k b^2 with positive integers a,b, for each k=1,...,n.

2, 17, 73, 73, 241, 241, 1009, 1009, 1009, 1009, 7561, 7561, 21961, 32356, 32356, 32356, 44641, 44641, 349924, 349924, 349924, 349924

1,1

Sequence A028372 considers primes with this property, but allowing for nonzero a,b (which obviously is irrelevant for n>2). Up to n=13, the terms of the present sequence are prime without imposing it explicitely and thus coincide with A028372 except for n=2.

a(1) = 2 = 1^2 + 1^2 is the least number of the sequence A000404 (sum of positive squares). a(2) = 17 = 1^2 + 4^2 = 3^2 + 2*2^2 is the least number in sequence A000404 to be in sequence A154777 (a^2+2b^2)as well. a(3) = 73 = 3^2 + 8^2 = 1^2 + 2*6^2 = 5^2 + 3*4^2 is the least number in the intersection of sequences A000404, A154777 and A092572 (a^2+3b^2).

(PARI) k=1; for( n=1, 10^9, forstep( c=k, 1, -1, for( b=1, sqrtint((n-1)\c), issquare(n-c*b^2) & next(2)); next(2)); print1(n", "); k++; n--)

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

more,nonn

M. F. Hasler (MHasler(AT)univ-ag.fr), Jan 27 2009

approved