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A071222
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Smallest k such that gcd(n,k) = gcd(n+1,k+1).
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8
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1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2
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OFFSET
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0,2
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COMMENTS
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a(n-1)+1 = A053669(n) = Smallest k >= 2 coprime to n = Smallest prime not dividing n.
Note that a(n) is equal to A235918(n+1) for the first 209 values of n. The first difference occurs at n=210 and A235921 lists the integers n for which a(n) differs from A235918(n+1).
(End)
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LINKS
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FORMULA
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Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A249270 - 1. - Amiram Eldar, Jul 26 2022
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MATHEMATICA
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sgcd[n_]:=Module[{k=1}, While[GCD[n, k]!=GCD[n+1, k+1], k++]; k]; Array[sgcd, 110] (* Harvey P. Dale, Jul 13 2012 *)
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PROG
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(PARI) for(n=1, 140, s=1; while(gcd(s, n)<gcd(n+1, s+1), s++); print1(s, ", "))
(Scheme) (define (A071222 n) (let loop ((k 1)) (cond ((= (gcd n k) (gcd (+ n 1) (+ k 1))) k) (else (loop (+ 1 k)))))) ;; Antti Karttunen, Jan 26 2014
(Haskell)
a071222 n = head [k | k <- [1..], gcd (n + 1) (k + 1) == gcd n k]
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CROSSREFS
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KEYWORD
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easy,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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