A282538 Odd integers n with the property that the largest prime factor of n^2+4 is less than n.

11, 29, 49, 59, 99, 111, 121, 127, 141, 161, 179, 199, 205, 211, 213, 219, 237, 247, 261, 283, 289, 309, 311, 335, 359, 369, 387, 393, 411, 417, 419, 433, 441, 469, 479, 485, 521, 523, 527, 535, 569, 581, 595, 603, 611, 619, 621, 633, 643, 679, 691, 705, 711, 715, 723, 729, 739, 741, 749, 759

Offset

1,1

Comments

Every Pythagorean prime p can be uniquely written as the sum of two positive integers a and b such that ab is congruent to 1 (mod p). If a>b, then the difference a-b must be an odd number; no number on this list can be said difference, and every positive odd integer NOT on this list is the difference of exactly one pair.

Links

Table of n, a(n) for n=1..60.

Example

Examples: 5 is not on this list, and 17-12=5 while 17+12=29 and (17)(12)==1 mod 29.  9 is not on this list, and 13-4=9 while 13+4=17 and (13)(4)==1 mod 17.  13 is not on this list, and 93-80=13 while 93+80=173 and (93)(80)==1 mod 173.  Note that 5^2+4=29, 9^2+4=85=17(5), and 13^2+4=173

Mathematica

fQ[n_] := FactorInteger[n^2 + 4][[-1, 1]] < n; Select[2 Range[380] - 1, fQ] (* Robert G. Wilson v, Feb 17 2017 *)

Prog

(PARI) isok(n) = (n%2) && vecmax(factor(n^2+4)[, 1]) < n; \\ Michel Marcus, Feb 18 2017

Crossrefs

Cf. A256011 (generated similarly, but for n^2+1 instead of n^2+4).

Sequence in context: A031338 A301621 A049229 * A236485 A039316 A364894

Adjacent sequences: A282535 A282536 A282537 * A282539 A282540 A282541

Keyword

nonn

Author

Michael Kaltman, Feb 17 2017

Extensions

a(22) onward from Robert G. Wilson v, Feb 17 2017

Status

approved