

A175932


Smallest prime p such that there exist exactly n integers b such that 1 < b < p and b^(p1) == 1 (mod p^2) or, equivalently, Fermat quotient q_p(b) == 0 (mod p).


3



2, 29, 11, 269, 487, 653, 5107, 103291, 40487, 2544079, 1093, 3511, 1006003
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OFFSET

0,1


COMMENTS



LINKS



EXAMPLE

a(5) = 653 since 653 is the smallest prime with exactly five bases b = 84, 120, 197, 287, 410.


PROG

(PARI) first_n_entries(n)=v=vector(n); toGo=n; forprime(p=2, , count=sum(b=2, p1, Mod(b, p^2)^(p1)==1); if(count<=(n1)&!v[count+1], v[count+1]=p; toGo; if(!toGo, return(v)))) \\ Jeppe Stig Nielsen, Jul 31 2015, changed to include a(0) = 2 by Jianing Song, Feb 05 2019


CROSSREFS



KEYWORD

hard,more,nonn


AUTHOR



EXTENSIONS



STATUS

approved



