A258045 - OEIS

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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).

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	`Table of n, a(n) for n=2..88.`
	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 A080234` `Adjacent sequences: A258042 A258043 A258044 * A258046 A258047 A258048`
	KEYWORD	`nonn,tabl`
	AUTHOR	`Felix Fröhlich, May 26 2015`
	EXTENSIONS	`Edited. - Wolfdieter Lang, Jun 29 2015`
	STATUS	`approved`

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Last modified March 11 12:59 EST 2017. Contains 283327 sequences.