A211181 Numbers n such that (n+1)^2 + n and (n+1)^2 - n are both prime.

1, 2, 3, 5, 8, 12, 14, 15, 20, 27, 38, 54, 59, 69, 75, 99, 119, 143, 147, 153, 162, 168, 173, 192, 194, 218, 245, 287, 293, 329, 342, 348, 357, 392, 395, 404, 447, 455, 489, 495, 500, 518, 540, 560, 572, 603, 605, 609, 624, 762, 768, 785, 855, 920, 993

Offset

1,2

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Sequences related to Legendre's conjecture - Jonathan Sondow, Feb 12 2013

Example

n=1,   (n+1)=2;   (n+1)^2=4;     4+1=5           and 4-1=3
n=173, (n+1)=174; (n+1)^2=30276; 30276+173=30449 and 30276-173=30103
n=192, (n+1)=193; (n+1)^2=37249; 37249+192=37441 and 37249-192-37057

Mathematica

Select[ Range[1000], PrimeQ[(# + 1)^2 + #] && PrimeQ[(# + 1)^2 - #] &] (* Jonathan Sondow, Feb 12 2013 *)

Prog

Input "n"'n:Lbl colorin:(n+1)^2-n->rtl:(n+1)^2+n->rtm:if IsPrime (rtm) and
isPrime (rtl) Then:Disp n:Pause:Endif:n+1->n:Goto colorin:EndPrgm
Texas Instruments Basic

Crossrefs

Sequence in context: A176746 A067288 A308075 * A028766 A342494 A022487

Adjacent sequences: A211178 A211179 A211180 * A211182 A211183 A211184

Keyword

nonn

Author

César Aguilera, Feb 11 2013

Extensions

More terms from Jonathan Sondow, Feb 12 2013

Status

approved