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 A253596 Numbers k such that A002313(m) is the greatest prime divisor of k^2 + 1 and A002313(m+1) is the greatest prime divisor of (k+1)^2 + 1 for some m. 0
 1, 7, 31, 293, 1936, 2244, 4158, 5744, 11573, 25242, 285202, 339354 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A002313 contains the primes congruent to 1 or 2 (mod 4). The corresponding indices m in A002313 are 1, 2, 6, 13, 69, 65, 322, 199, 130, 46, 1471, 866, ... The corresponding primes A002313(m) are 2, 5, 37, 101, 809, 761, 4877, 2777, 1709, 509, 26821, 14957, ... LINKS Table of n, a(n) for n=1..12. EXAMPLE 31 is in the sequence because 31^2 + 1 = 2*13*37 and 32^2 + 1 = 5*5*41 with the property that 37 = A002313(6) and 41 = A002313(7). MAPLE with(numtheory): nn:=500000:print(1): for n from 1 to nn do: p:=n^2+1:x:=factorset(p):n0:=nops(x):p1:=x[n0]: q:=(n+1)^2+1:y:=factorset(q):n1:=nops(y):p2:=y[n1]:ii:=0: for j from 2 by 2 to 1000 while(ii=0) do: pp:=p1+j: if type(pp, prime)=true and irem(pp, 4)=1 then p3:=pp:ii:=1: else fi: od: if p3=p2 then print(n): else fi: od: MATHEMATICA lst={}; Do[If[Mod[Prime[i], 4]==1||Mod[Prime[i], 4]==2, AppendTo[lst, Prime[i]]], {i, 1, 1000}]; Do[Do[If[FactorInteger[n^2+1][[-1]][[1]]==Part[lst, j]&&FactorInteger[(n+1)^2+1][[-1]][[1]]==Part[lst, j+1], Print[n]], {n, 1, 20000}], {j, 1, 999}] CROSSREFS Cf. A002313, A014442. Sequence in context: A143564 A352411 A344787 * A298958 A153028 A276667 Adjacent sequences: A253593 A253594 A253595 * A253597 A253598 A253599 KEYWORD nonn,more AUTHOR Michel Lagneau, Jan 05 2015 STATUS approved

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Last modified June 20 22:01 EDT 2024. Contains 373532 sequences. (Running on oeis4.)