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 A258045 Table T(b, m) of largest exponents k such that for p = prime(m) and base b > 1 the congruence b^(p-1) == 1 (mod p^k) is satisfied, or 0 if no such k exists, read by antidiagonals (downwards). 3
 0, 1, 1, 1, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,10 COMMENTS Table starts b=2:  0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=3:  1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=4:  0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=5:  2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=6:  0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=7:  1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=8:  0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=9:  3, 0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=10: 0, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=11: 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=12: 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=13: 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ... b=14: 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1 ... b=15: 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=16: 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... b=17: 4, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 ... b=18: 0, 0, 2, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1 ... b=19: 1, 2, 1, 3, 1, 2, 1, 0, 1, 1, 1, 1, 1, 2 ... b=20: 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ... .... a(n) > 1 if b appears in row k, column n of the table in A257833 for k > 1 and n > 1. LINKS FORMULA a(n, m) = T(m+1, n-m), n >=2, m = 1, 2, ..., n-1. - Wolfdieter Lang, Jun 29 2015 EXAMPLE T(3, 5) = 2, because the largest Wieferich exponent of prime(5) = 11 in base 3 is 2. The triangle a(n ,m) begins:   m 1 2 3 4 5 6 7 8 9 10 11 ... n 2   0 3   1 1 4   1 0 0 5   1 1 1 2 6   1 1 1 1 0 7   1 2 1 0 0 1 8   1 1 1 1 1 1 0 9   1 1 1 1 1 2 2 3 10  1 1 1 1 1 0 1 0 0 11  1 1 1 1 1 1 1 1 2  1 12  1 1 1 1 1 1 1 1 0  1  0 ... PROG (PARI) for(b=2, 20, forprime(p=1, 70, k=0; while(Mod(b, p^k)^(p-1)==1, k++); if(k > 0, k--); print1(k, ", ")); print("")) CROSSREFS Cf. A001220, A257833. Sequence in context: A037818 A087116 A033264 * A239302 A256983 A330720 Adjacent sequences:  A258042 A258043 A258044 * A258046 A258047 A258048 KEYWORD nonn,tabl AUTHOR Felix FrÃ¶hlich, May 26 2015 EXTENSIONS Edited. - Wolfdieter Lang, Jun 29 2015 STATUS approved

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Last modified September 19 13:56 EDT 2020. Contains 337178 sequences. (Running on oeis4.)