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A135376
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a(n) is the smallest prime that does not divide n(n+1)/2.
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1
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2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 5, 5, 2, 2, 7, 3, 2, 2, 3, 11, 2, 2, 5, 7, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 11, 5, 2, 2, 7, 3, 2, 2, 3, 7, 2, 2, 5, 5, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 7, 7, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 5, 5, 2, 2, 7, 3, 2, 2, 3, 7, 2, 2, 5, 11, 2, 2, 5, 3, 2, 2, 3, 5, 2, 2, 7, 5, 2, 2, 7, 3, 2, 2, 3
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OFFSET
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1,1
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COMMENTS
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The sums of the first 10^k terms, for k = 1, 2, ..., are 28, 354, 3596, 36026, 360402, 3604134, 36041392, 360413970, 3604140072, 36041400856, ... . Apparently, the asymptotic mean of this sequence is limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3.604140... . - Amiram Eldar, Sep 10 2022
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LINKS
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FORMULA
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a(4n+1) = a(4n+2) = 2 for all nonnegative integers n.
a(n) = A053670(n) for all n congruent to 0 or 3 (mod 4).
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EXAMPLE
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The 11th triangular number is 66 = 2*3*11. 5 is the smallest prime that is coprime to 66, so a(11) = 5.
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MAPLE
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A135376 := proc(n) local T, p ; T := n*(n+1)/2 ; p := 2 ; while T mod p = 0 do p := nextprime(p) ; od: RETURN(p) ; end: seq(A135376(n), n=1..120) ; # R. J. Mathar, Dec 11 2007
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MATHEMATICA
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a = {}; For[n = 1, n < 80, n++, j = 1; While[Mod[n*(n + 1)/2, Prime[j]] == 0, j++ ]; AppendTo[a, Prime[j]]]; a (* Stefan Steinerberger, Dec 10 2007 *)
sp[n_]:=Module[{p=2}, While[Mod[n, p]==0, p=NextPrime[p]]; p]; sp[#]&/@ Accumulate[ Range[110]] (* Harvey P. Dale, Jul 26 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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