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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 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 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

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Last modified July 30 10:27 EDT 2021. Contains 346359 sequences. (Running on oeis4.)