

A269668


Smallest k >= 0 such that neither (k + 1)*n  k nor (k + 1)*n + k is prime.


2



0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 7, 0, 1, 0, 0, 0, 1, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 10, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 3, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 3
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OFFSET

1,2


COMMENTS

Numbers n such that a(n) = m: 2, 31, 41, 131, 157, ... (for m = 2);
3, 53, 83, 97, 139, ... (for m = 3); 19, 23, 79, 191, ... (for m = 4), ...


LINKS



EXAMPLE

For n = 2, k = 0: (0 + 1)*2  0 = 2 is prime and (0 + 1)*2 + 0 = 2 is prime; for n = 2, k = 1: (1 + 1)*2  1 = 3 is prime and (1 + 1)*2 + 1 = 5 is prime; for n = 2, k = 2: (2 + 1)*2  2 = 4 is composite and (2 + 1)*2 + 2 = 6 is composite, so a(2) = 2.


MATHEMATICA

Table[SelectFirst[Range[0, 120], And[! PrimeQ[n (# + 1)  #], ! PrimeQ[n (# + 1) + #]] &], {n, 120}] (* Michael De Vlieger, Mar 04 2016, Version 10 *)


PROG

(PARI) A269668(n) = {my(k=0); while (isprime((k+1)*nk)  isprime((k+1)*n+k), k++); k; } \\ Michel Marcus, Apr 04 2016, corrected by Antti Karttunen, Dec 27 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



