

A282538


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


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 ab 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 1712=5 while 17+12=29 and (17)(12)==1 mod 29. 9 is not on this list, and 134=9 while 13+4=17 and (13)(4)==1 mod 17. 13 is not on this list, and 9380=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 A082108
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



