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A103689
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a(n) is the least k such that either k*n - 1 or k*n + 1 (or both) is prime.
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6
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1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 4, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 6, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 6, 1, 6, 1, 2, 2, 2, 1, 4, 1, 2, 1, 4, 1, 4, 1, 2, 2, 4, 1, 2, 1, 2, 1, 2, 1, 6, 2, 2, 1, 2, 1, 2, 3, 4, 3, 2, 1, 2, 1, 2, 1, 6, 1, 6, 1, 2
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OFFSET
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1,5
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LINKS
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FORMULA
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a(A002110(n)/3+3) >= ceiling((prime(n+1)-1)/3) for n >= 2. Equality holds for n = 2, 4, 6, 8, 10, 12, 22, 25, 31, 116, 155, 156, 197, ... . - Pontus von Brömssen, Oct 16 2021
a(A002110(n)/3-3) >= ceiling((prime(n+1)-1)/3) for n >= 3. Equality holds for n = 3, 4, 5, 6, 7, 9, 39, 51, 59, 65, 98, 311, ... . - Pontus von Brömssen, Oct 19 2021
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MATHEMATICA
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f[n_] := Block[{k = 1}, While[ ! PrimeQ[k*n - 1] && ! PrimeQ[k*n + 1], k++ ]; k]; Table[ f[n], {n, 105}] (* Robert G. Wilson v, Feb 12 2005 *)
lk[n_]:=Module[{k=1}, While[NoneTrue[k*n+{1, -1}, PrimeQ], k++]; k]; Array[ lk, 120] (* The program uses the NoneTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 01 2016 *)
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PROG
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(Haskell)
a103689 n = min (a053989 n) (a034693 n)
(PARI) a(n) = my(k=1); while (!isprime(k*n+1) && !isprime(k*n-1), k++); k; \\ Michel Marcus, Oct 18 2021
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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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