A173297 Numbers k such that exactly one of k^2 + k - 1 and k^2 + k + 1 is prime.

1, 4, 9, 10, 11, 12, 13, 14, 16, 17, 19, 26, 27, 28, 30, 31, 33, 35, 39, 44, 45, 46, 48, 53, 55, 56, 57, 60, 62, 64, 65, 68, 69, 70, 71, 75, 76, 77, 78, 80, 83, 85, 86, 90, 93, 94, 96, 99, 100, 103, 105, 110, 111, 114, 115, 117, 119, 120, 125, 126, 130, 134, 140, 143, 144

Offset

1,2

Comments

Numbers k such that either k-th oblong number-+1 is prime.

Indices k such that A002378(k)+1 or A002378(k)-1 is prime, but not both. - R. J. Mathar, Feb 21 2010

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

isA173297 := proc(n) local p, pplus, pmin ; pmin := isprime(n*(1+n)-1) ; pplus := isprime(n*(1+n)+1) ; if pmin <> pplus then return true; else return false; end if; end proc: for n from 1 to 300 do if isA173297(n) then printf("%d, ", n) ; end if; end do ; # R. J. Mathar, Feb 21 2010

Mathematica

Select[Range[144], Xor[PrimeQ[#^2+#-1], PrimeQ[#^2+#+1]] &] (* Stefano Spezia, Jun 01 2026 *)

Crossrefs

Cf. A002378, A088485.

Sequence in context: A088037 A071768 A301478 * A161913 A396579 A020673

Adjacent sequences: A173294 A173295 A173296 * A173298 A173299 A173300

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Feb 15 2010

Extensions

46 and 86 inserted by R. J. Mathar, Feb 21 2010

Edited by Charles R Greathouse IV, Mar 24 2010

Status

approved