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A090414 Triangular array read by rows, 1<=k<=n: T(n,k) = smallest prime that in binary representation is not contained in n^k.

%I A090414 #12 Mar 01 2020 07:17:26
%S A090414 2,3,3,2,3,7,3,3,3,3,3,5,11,5,7,5,3,7,3,5,7,2,5,13,7,11,13,17,3,3,3,3,
%T A090414 3,3,3,3,3,3,7,7,11,19,19,17,13,3,5,11,5,7,11,7,17,17,13,7,5,7,5,23,7,
%U A090414 13,7,7,17,17,5,3,7,3,5,7,7,7,5,11,17,19
%N A090414 Triangular array read by rows, 1<=k<=n: T(n,k) = smallest prime that in binary representation is not contained in n^k.
%H A090414 Jinyuan Wang, <a href="/A090414/b090414.txt">Rows n = 1..100 of triangle, flattened</a>
%e A090414 Triangle begins:
%e A090414 2;
%e A090414 3, 3;
%e A090414 2, 3,  7;
%e A090414 3, 3,  3, 3;
%e A090414 3, 5, 11, 5,  7;
%e A090414 5, 3,  7, 3,  5,  7;
%e A090414 2, 5, 13, 7, 11, 13, 17;
%e A090414 ..
%o A090414 (PARI) T(n,k) = {my(d=binary(n^k), v); forprime(p=2, oo, v=binary(p); if(#v>#d || sum(i=1, #d-#v+1, v==vector(#v, j, d[i+j-1]))==0, return(p))); } \\ _Jinyuan Wang_, Mar 01 2020
%Y A090414 Cf. A004676, A007088, A075363.
%K A090414 nonn,base,tabl
%O A090414 1,1
%A A090414 _Reinhard Zumkeller_, Nov 30 2003
%E A090414 More terms from _Jinyuan Wang_, Mar 01 2020