A233443 Primes that are exactly between the nearest square and the nearest triangular number.

2, 5, 23, 47, 193, 389, 1667, 8807, 9431, 10177, 10597, 10847, 11831, 13411, 17183, 22433, 29201, 33893, 36073, 38321, 40093, 42461, 48991, 50131, 54287, 54851, 57037, 63347, 65183, 67121, 71917, 87803, 88607, 91291, 94847, 104491, 108293, 112163, 116101, 117167, 122033

Offset

1,1

Comments

A subsequence of A233074.

Links

Table of n, a(n) for n=1..41.

Mathematica

nearestTri[n_] := Block[{a = Floor@ Sqrt[ 2n - 1]}, If[ 4n < a (a + 3), a (a - 1)/2, a (a + 1)/2]]; nearestSq[n_] :=  Block[{a = Floor@ Sqrt@ n}, If[a^2 + a + 1/2 > n, a^2, a^2 + 2 a + 1]]; Select[ Prime@ Range@ 12000, 2# == nearestSq@# + nearestTri@# &] (* Robert G. Wilson v, Aug 01 2014 *)

Prog

(PARI) lista(nn) = {forprime(p=2, nn, sqp = sqrtint(p); ps = sqp^2; ns = (sqp+1)^2; sqt = floor((sqrt(8*p+1) - 1)/2); pt = sqt*(sqt+1)/2; nt = (sqt+2)*(sqt+1)/2; if (((ds=p-ps) < (ns-p)) && ((dt=(nt-p)) <= p-pt) && (ds == dt), print1(p, ", "), if (((ds=ns-p) < (p-ps)) && ((dt=(p-pt)) < nt-p) && (ds == dt), print1(p, ", ")); ); ); } \\ Michel Marcus, Aug 11 2014

Crossrefs

Cf. A000040, A000217, A000290, A233074.

Sequence in context: A215278 A126975 A175444 * A156314 A308055 A173396

Adjacent sequences: A233440 A233441 A233442 * A233444 A233445 A233446

Keyword

nonn

Author

Alex Ratushnyak, Dec 09 2013

Extensions

Corrected by Alex Ratushnyak, Jun 08 2014

Status

approved