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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
2, 29, 11, 269, 487, 653, 5107, 103291, 40487, 2544079, 1093, 3511, 1006003 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

Table of n, a(n) for n=0..12.

Richard Fischer, Extreme first bases

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, 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

CROSSREFS

Cf. A001220, A130912, A248865, A242830.

Subset of A134307.

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

Sequence in context: A180423 A090497 A128371 * A225544 A153655 A153657

Adjacent sequences:  A175929 A175930 A175931 * A175933 A175934 A175935

KEYWORD

hard,more,nonn

AUTHOR

Max Alekseyev, Oct 24 2010

EXTENSIONS

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

STATUS

approved

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Last modified August 8 23:02 EDT 2020. Contains 336300 sequences. (Running on oeis4.)