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
Keywords
Programs
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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 *) -
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
Extensions
Corrected by Alex Ratushnyak, Jun 08 2014
Comments