A245522 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, 11, 15, 15, 31, 39, 373, 1285, 1285, 1285, 2119, 2119, 15605, 29223, 52225, 52225, 186157, 186157, 1378927, 3137489, 4189897, 4189897, 10373543, 50359121, 50359121, 50359121, 490844965, 605616359, 605616359, 605616359, 3351375815, 3351375815, 5812974437

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..33.

Example

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.

Mathematica

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 *)

Crossrefs

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

Sequence in context: A235913 A132363 A134629 * A358226 A030715 A056247

Adjacent sequences: A245519 A245520 A245521 * A245523 A245524 A245525

Keyword

nonn,base

Author

Chai Wah Wu, Jul 24 2014

Extensions

a(23)-a(33) from Amiram Eldar, May 13 2019

Status

approved