A175932 Smallest prime p such that there exist exactly n integers b such that 1 < b < p and b^(p-1) == 1 (mod p^2) or, equivalently, Fermat quotient q_p(b) == 0 (mod p).

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

Offset: 0

Author

Max Alekseyev, Oct 24 2010

Keywords

• hard
• more
• nonn

Comments

a(n) is the smallest prime p such that A242830(PrimePi(p)) = n, PrimePi = A000720. - Jianing Song, Jan 27 2019

Examples

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

Links

• Richard Fischer, Extreme first bases

Crossrefs

Cf. A001220, A130912, A248865, A242830.

Subset of A134307.

Cf. also A255203, A255204, A255205, A255206, A255207, A255208, A255209, A255210.

Programs

PARI

first_n_entries(n)=v=vector(n); toGo=n; forprime(p=2, , count=sum(b=2, p-1, Mod(b, p^2)^(p-1)==1); if(count<=(n-1)&!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

Extensions

a(0) = 2 prepended by Jianing Song, Jan 27 2019