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A035093 Smallest k - dependent on n - such that (n!)*k+1 is prime where k is the subscript of the progressions. 6
1, 1, 1, 3, 2, 3, 3, 4, 3, 3, 1, 2, 3, 13, 7, 4, 5, 2, 7, 17, 15, 18, 3, 6, 3, 16, 1, 4, 7, 20, 8, 3, 9, 5, 2, 7, 1, 3, 10, 3, 1, 29, 7, 9, 45, 8, 3, 6, 35, 66, 2, 20, 2, 4, 25, 52, 14, 34, 24, 6, 10, 22, 38, 16, 20, 91, 69, 12, 19, 20, 21, 42, 1, 5, 33, 77, 1, 2, 12, 29, 193, 74, 40, 55, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This is one possible generalization of "the least prime problem" for nk+1 arithmetic progression when n is replaced by n!, a special difference.

LINKS

Table of n, a(n) for n=1..85.

Index entries for sequences related to primes in arithmetic progressions

EXAMPLE

a(7)=3 because in progression of 5040k+1 the terms 5041 and 10081 are not prime and so 15121 is the first prime.

MATHEMATICA

Table[k = 1; While[! PrimeQ[1 + k*n!], k++]; k, {n, 85}] (* T. D. Noe, Nov 04 2013 *)

CROSSREFS

Analogous case is A034693. Special case for k=1 is A002981.

Sequence in context: A130970 A144733 A091460 * A292511 A238872 A260195

Adjacent sequences:  A035090 A035091 A035092 * A035094 A035095 A035096

KEYWORD

nonn

AUTHOR

Labos Elemer

EXTENSIONS

a(80) corrected by Alex Ratushnyak, Nov 03 2013

STATUS

approved

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Last modified September 18 20:51 EDT 2019. Contains 327181 sequences. (Running on oeis4.)