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.
2, 5, 3, 7, 17, 5, 19, 131, 7, 7, 127, 659, 19, 19, 11, 911, 503, 127, 127, 3, 13, 7331, 9833, 911, 911, 17, 19, 17, 167149, 49603, 7331, 7331, 131, 127, 131, 19, 387749, 327317, 167149, 167149, 659, 911, 659, 127, 23, 17153317, 13900147, 387749, 387749, 503
Offset: 1
Examples
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. Array starts: 2 5 7 19 127 911 7331 167149 387749 17153317 ... 3 17 131 659 503 9833 49603 327317 13900147 144229223 ... 5 7 19 127 911 7331 167149 387749 17153317 ... 7 19 127 911 7331 167149 387749 17153317 432383657 ... 11 3 17 131 659 503 9833 49603 327317 ... 13 19 127 911 7331 167149 387749 ... 17 131 659 503 9833 49603 327317 ... 19 127 911 7331 167149 387749 17153317 ... 23 263 79 31 229 503 ... 29 41 313 1499 941 12011 ... ...
Programs
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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(""))