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A255901 Smallest base b such that there exist exactly n Wieferich primes (primes p satisfying b^(p-1) == 1 (mod p^2)) less than b. 2
5, 17, 19, 116, 99, 361, 1451, 1693, 10768, 13834, 208301, 548291 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For all n a(n) <= A252232(n).

a(n) == A252232(n) iff a(n) is prime.

From Robert G. Wilson v, Mar 11 2015: (Start)

n        b  p

1:       5 {2}

2:      17 {2, 3}

3:      19 {3, 7, 13}

4:     116 {3, 7, 19, 47}

5:      99 {5, 7, 13, 19, 83}

6:     361 {2, 3, 7, 13, 43, 137}

7:    1451 {5, 7, 11, 13, 83, 173, 1259}

8:    1693 {2, 3, 5, 11, 31, 37, 61, 109}

9:   10768 {5, 11, 17, 19, 79, 101, 139, 6343, 10177}

10:  13834 {3, 11, 17, 19, 43, 139, 197, 2437, 5849, 6367

11: 208301 {2, 5, 29, 47, 59, 113, 661, 8209, 13679, 15679, 55633}

12: 548291 {7, 11, 19, 29, 31, 37, 97, 211, 547, 911, 2069, 28927}

... (End)

LINKS

Table of n, a(n) for n=1..12.

MATHEMATICA

f[n_] := Block[{b = 2, p}, While[p = Prime@ Range@ PrimePi[b - 1]; Count[ PowerMod[b, p - 1, p^2], 1] != n, b++]; b]; Array[f, 11] (* Robert G. Wilson v, Mar 11 2015 *)

PROG

(PARI) for(n=1, 10, b=2; while(b > 0, i=0; forprime(p=1, b, if(Mod(b, p^2)^(p-1)==1, i++)); if(i==n, print1(b, ", "); break({1})); b++))

CROSSREFS

Cf. A252232, A255885.

Sequence in context: A171255 A304540 A306125 * A098333 A252232 A162862

Adjacent sequences:  A255898 A255899 A255900 * A255902 A255903 A255904

KEYWORD

nonn,more

AUTHOR

Felix Fröhlich, Mar 10 2015

EXTENSIONS

a(11) from Robert G. Wilson v, Mar 11 2015

a(12) from Robert G. Wilson v, Mar 12 2015

STATUS

approved

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Last modified February 24 07:44 EST 2020. Contains 332199 sequences. (Running on oeis4.)