A180508 Numbers k such that k^2 + 1 = p*q, p and q primes and | p-q | <= k.

3, 8, 46, 50, 76, 100, 144, 266, 274, 334, 504, 516, 526, 566, 670, 726, 756, 810, 836, 844, 1064, 1086, 1164, 1250, 1300, 1714, 1740, 1800, 1826, 1834, 1946, 1950, 2014, 2194, 2220, 2440, 2450, 2466, 2494, 2560, 2610

Offset

1,1

Comments

|p - q| = k for k = 3, 8, 144.

Links

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

Example

46 is in the sequence because 46^2 + 1 = 29*73, and 73-29 = 44 < 46.

Maple

with(numtheory):for n from 1 to 4000 do: x:=n^2+1:y:=factorset(x):yy:=bigomega(x):if
  yy=2 and (y[2]-y[1] < n or y[2]-y[1] = n) then printf(`%d, `, n):else fi:od:

Crossrefs

Cf. A134406 A027862 A134407 A002522 A005574.

Sequence in context: A182390 A132103 A334316 * A040018 A019016 A063859

Adjacent sequences: A180505 A180506 A180507 * A180509 A180510 A180511

Keyword

nonn

Author

Michel Lagneau, Jan 20 2011

Status

approved