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Index of the smallest prime where n consecutive trailing digits of the index written in binary match n consecutive trailing digits in the prime when written in binary.
3

%I #13 May 13 2019 05:24:51

%S 3,11,15,15,31,39,373,1285,1285,1285,2119,2119,15605,29223,52225,

%T 52225,186157,186157,1378927,3137489,4189897,4189897,10373543,

%U 50359121,50359121,50359121,490844965,605616359,605616359,605616359,3351375815,3351375815,5812974437

%N Index of the smallest prime where n consecutive trailing digits of the index written in binary match n consecutive trailing digits in the prime when written in binary.

%C Similar to A133589, except the comparison is done in binary.

%e a(6) = 39 since 39 in binary is 100111, the 39th prime is 167, or 10100111 in binary and the last 6 digits of these two binary numbers coincide.

%t f[n_] := Module[{p = Prime[n]}, m = IntegerExponent[p - n, 2]; If[n < 2^m, Length[IntegerDigits[n, 2]], m]]; fm = 0; s = {}; Do[f1 = f[n]; If[f1 > fm, s = Join[s, Table[n, {f1 - fm}]]; fm = f1], {n, 1, 10^6}]; s (* _Amiram Eldar_, May 13 2019 *)

%Y Cf. A245520, A245521, A245523, A133583, A133584, A133589, A133590.

%K nonn,base

%O 1,1

%A _Chai Wah Wu_, Jul 24 2014

%E a(23)-a(33) from _Amiram Eldar_, May 13 2019