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A249162 Square array A(p, b) read by antidiagonals in which rows are indexed by successive prime numbers p_i and row b(p_i) gives the smallest prime base b_n to which q = (p_i, b_(n-1)) is a Wieferich prime. 0

%I

%S 2,5,3,7,17,5,19,131,7,7,127,659,19,19,11,911,503,127,127,3,13,7331,

%T 9833,911,911,17,19,17,167149,49603,7331,7331,131,127,131,19,387749,

%U 327317,167149,167149,659,911,659,127,23,17153317,13900147,387749,387749,503

%N Square array A(p, b) read by antidiagonals in which rows are indexed by successive prime numbers p_i and row b(p_i) gives the smallest prime base b_n to which q = (p_i, b_(n-1)) is a Wieferich prime.

%C Array starts:

%C 2 5 7 19 127 911 7331 167149 387749 17153317 ...

%C 3 17 131 659 503 9833 49603 327317 13900147 144229223 ...

%C 5 7 19 127 911 7331 167149 387749 17153317 ...

%C 7 19 127 911 7331 167149 387749 17153317 432383657 ...

%C 11 3 17 131 659 503 9833 49603 327317 ...

%C 13 19 127 911 7331 167149 387749 ...

%C 17 131 659 503 9833 49603 327317 ...

%C 19 127 911 7331 167149 387749 17153317 ...

%C 23 263 79 31 229 503 ...

%C 29 41 313 1499 941 12011 ...

%C ...

%e A(6,4) = 911, since the 6th prime is 13 and the smallest prime Wieferich base for 13 is 19. Applying this procedure recursively to the resulting bases a total of b-1 = 3 times leads to 911.

%o (PARI) forprime(p=1, 30, b=1; i=0; q=p; print1(p, ", "); while(i < 6, b++; if(Mod(b, q^2)^(q-1)==1 && isprime(b), print1(b, ", "); q=b; b=1; i++)); print(""))

%Y Cf. A001220, A244249.

%Y Second column of table is A125636.

%K nonn,tabl

%O 1,1

%A _Felix Fröhlich_, Oct 22 2014

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Last modified July 27 18:27 EDT 2021. Contains 346308 sequences. (Running on oeis4.)