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 A217448 Least k > 0 such that 1 + n^2 and 1 + (n+k)^2 have the same smallest prime factor. 0
 2, 6, 2, 26, 2, 74, 2, 4, 2, 404, 2, 6, 2, 366, 2, 514, 2, 4, 2, 1564, 2, 6, 2, 1106, 2, 4010, 2, 4, 2, 34, 2, 6, 2, 10, 2, 2594, 2, 4, 2, 22334, 2, 6, 2, 16, 2, 58, 2, 4, 2, 64, 2, 6, 2, 29062, 2, 18710, 2, 4, 2, 10, 2, 6, 2, 42, 2, 17428, 2, 4, 2, 16, 2, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Alternate title: Least k > 0 such that A089120(n) = A089120(n+k). A089120(n): smallest prime factor of n^2 + 1. Conjecture: a(n) exists for all n. LINKS EXAMPLE a(10) = 404 because 10^2 + 1 = 101, (10+404)^2+1 = 101*1697 so A089120(10) = A089120(414) = 101; a(170) = 404274 because 170^2 + 1 = 28901, (170+404274)^2+1 = 163574949137 = 28901* 5659837 so A089120(170) = A089120(40444) = 28901. MAPLE with(numtheory):T:=array(1..100): for n from 1 to 100 do:x:=factorset(n^2+1):n1:=nops(x): T[n] := x[1]:od:for a from 1 to 80 do:p:=T[a]:ii:=0:for k from 1 to 50000 while(ii=0) do: z:=factorset((a+k)^2+1): n2:=nops(z):if z[1]=p then printf(`%d, `, k):ii:=1:else fi:od:od: MATHEMATICA sspf[n_]:=Module[{c=FactorInteger[1+n^2][[1, 1]], k=1}, While[ FactorInteger[ 1+ (n+k)^2][[1, 1]]!=c, k++]; k]; Array[sspf, 80] (* Harvey P. Dale, Oct 12 2012 *) CROSSREFS Cf. A089120, A217393, A014442. Sequence in context: A125032 A076743 A131980 * A280705 A027760 A141056 Adjacent sequences:  A217445 A217446 A217447 * A217449 A217450 A217451 KEYWORD nonn AUTHOR Michel Lagneau, Oct 03 2012 STATUS approved

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Last modified May 24 10:48 EDT 2019. Contains 323529 sequences. (Running on oeis4.)