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A261625 Number of primes p <= n such that (p-1)*n+1 is prime. 1
0, 1, 1, 1, 1, 2, 2, 1, 2, 3, 2, 2, 4, 1, 4, 3, 1, 5, 2, 2, 5, 4, 3, 3, 4, 3, 5, 6, 3, 5, 3, 2, 6, 5, 5, 5, 3, 2, 5, 6, 3, 4, 6, 2, 7, 9, 2, 5, 5, 3, 9, 7, 1, 5, 7, 5, 5, 8, 2, 8, 7, 3, 8, 7, 5, 7, 6, 3, 6, 9, 5, 9, 7, 4, 6, 8, 3, 8, 9, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
Conjecture: a(n) > 0 for all n > 1.
LINKS
Zhi-Wei Sun, Conjectures involving primes and quadratic forms, arXiv:1211.1588 [math.NT], 2012-2015.
EXAMPLE
a(53) = 1 since 3 and (3-1)*53+1 = 107 are both prime.
MATHEMATICA
Do[r=0; Do[If[PrimeQ[(Prime[k]-1)n+1], r=r+1], {k, 1, PrimePi[n]}]; Print[n, " ", r]; Continue, {n, 1, 80}]
PROG
(PARI) a(n) = my(nb=0); forprime(p=2, n, if (isprime((p-1)*n+1), nb++)); nb; \\ Michel Marcus, Aug 27 2015
CROSSREFS
Sequence in context: A091972 A025833 A200647 * A237284 A294186 A294185
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Aug 27 2015
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)