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 A248527 Numbers n such that the smallest prime divisor of n^2+1 is 13. 11
 34, 44, 60, 70, 86, 96, 164, 174, 190, 200, 216, 226, 294, 304, 320, 330, 346, 356, 424, 434, 450, 460, 476, 486, 554, 564, 580, 590, 606, 616, 684, 694, 710, 720, 736, 746, 814, 824, 840, 850, 866, 876, 944, 954, 970, 980, 996, 1006, 1074, 1084, 1100, 1110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Or numbers n such that the smallest prime divisor of A002522(n) is A002313(3). a(n) == 8 (mod 26) if n is odd and a(n) == 18 (mod 26) if n is even. It is interesting to observe that a(n) is given by a linear formula (see the formula below). LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA {a(n)} = {8+(k + m)*26} union {18+(k + m)*26} for m = 0, 5, 10,...,5p,... and k = 1, 2, 3 (values in increasing order). EXAMPLE 34 is in the sequence because 34^2+1= 13*89. MAPLE * first program * with(numtheory):p:=13:    for n from 1 to 1000 do:     if factorset(n^2+1)[1] = p then printf(`%d, `, n):     else     fi:    od: * second program using the formula* for n from 0 to 100 by 5 do:    for k from 1 to 3 do:      x:=8+(k+n)*26:y:=18+(k+n)*26:      printf(`%d, `, x):printf(`%d, `, y):    od:   od: MATHEMATICA lst={}; Do[If[FactorInteger[n^2+1][[1, 1]]==13, AppendTo[lst, n]], {n, 2, 2000}]; lst p = 13; ps = Select[Range[p - 1], Mod[#, 4] != 3 && PrimeQ[#] &]; Select[Range[1200], Divisible[(nn = #^2 + 1), p] && ! Or @@ Divisible[nn, ps] &] (* Amiram Eldar, Aug 16 2019 *) PROG (PARI) isok(n) = factor(n^2+1)[1, 1] == 13; \\ Michel Marcus, Oct 08 2014 (MAGMA) [n: n in [2..3000] | PrimeDivisors(n^2+1)[1] eq 13]; // Bruno Berselli, Oct 08 2014 CROSSREFS Cf. A002522, A089120, A002313. Sequence in context: A044020 A217276 A076772 * A206262 A302457 A063470 Adjacent sequences:  A248524 A248525 A248526 * A248528 A248529 A248530 KEYWORD nonn AUTHOR Michel Lagneau, Oct 08 2014 STATUS approved

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Last modified December 5 05:36 EST 2021. Contains 349530 sequences. (Running on oeis4.)