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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 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 FrÃ¶hlich, 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 May 7 12:05 EDT 2021. Contains 343650 sequences. (Running on oeis4.)