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A244249
Table A(n,k) in which n-th row lists in increasing order all bases b to which p = prime(n) is a Wieferich prime (i.e., b^(p-1) is congruent to 1 mod p^2), read by antidiagonals.
15
5, 9, 8, 13, 10, 7, 17, 17, 18, 18, 21, 19, 24, 19, 3, 25, 26, 26, 30, 9, 19, 29, 28, 32, 31, 27, 22, 38, 33, 35, 43, 48, 40, 23, 40, 28, 37, 37, 49, 50, 81, 70, 65, 54, 28, 41, 44, 51, 67, 94, 80, 75, 62, 42, 14, 45, 46, 57, 68, 112, 89, 110, 68, 63, 41, 115
OFFSET
1,1
LINKS
EXAMPLE
Table starts with:
p = 2: 5, 9, 13, 17, 21, 25, 29, 33, ...
p = 3: 8, 10, 17, 19, 26, 28, 35, 37, ...
p = 5: 7, 18, 24, 26, 32, 43, 49, 51, ...
p = 7: 18, 19, 30, 31, 48, 50, 67, 68, ...
p = 11: 3, 9, 27, 40, 81, 94, 112, 118, ...
p = 13: 19, 22, 23, 70, 80, 89, 99, 146, ...
p = 17: 38, 40, 65, 75, 110, 131, 134, 155, ...
MAPLE
A:= proc(n, k) option remember; local p, b;
p:= ithprime(n);
for b from 1 +`if`(k=1, 1, A(n, k-1))
while b &^ (p-1) mod p^2<>1
do od; b
end:
seq(seq(A(n, 1+d-n), n=1..d), d=1..14); # Alois P. Heinz, Jul 02 2014
MATHEMATICA
A[n_, k_] := A[n, k] = Module[{p, b}, p = Prime[n]; For[b = 1 + If[k == 1, 1, A[n, k-1]], PowerMod[b, p-1, p^2] != 1, b++]; b]; Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 14}] // Flatten (* Jean-François Alcover, Mar 09 2015, after Alois P. Heinz *)
PROG
(PARI) forprime(p=2, 10^1, print1("p=", p, ": "); for(a=2, 10^2, if(Mod(a, p^2)^(p-1)==1, print1(a, ", "))); print(""))
CROSSREFS
First column of table is A039678.
Main diagonal gives A280721.
Sequence in context: A077771 A019754 A315120 * A353602 A123600 A063623
KEYWORD
nonn,tabl
AUTHOR
Felix Fröhlich, Jun 23 2014
STATUS
approved