# [seqfan] request for help with A036952

N. J. A. Sloane njas at research.att.com
Fri Mar 12 19:20:18 CET 2010

```Dear Seq Fans,  Gerald Hillier asked me to clarify the definition of A036952.
The definition was:
%S A036952 3,5,23,47,89,101,149,157,163,173,179,185,199,229,247,253,295,313,329,
%T A036952 331,355,367,379,383,405,425,443,453,457,471,523,533,539,565,583,587,
%U A036952 595,631,643,647,653,659,671,675,689,703,709,755,781,785,815,841,855
%N A036952 Primes with digits (0,1) taken as base 2 and converted to base 10.
%C A036952 The sequence is unexpectedly(?) rich in primes.
%e A036952 a(n)=313 -> is 100111001{2} -> 100111001{10} is prime.
%Y A036952 Cf. A020449, A036953-A036964.
...
%A A036952 Patrick De Geest (pdg(AT)worldofnumbers.com), Jan 04 1999.

I looked at hastily, and changed it to:

%S A036952 3,5,23,47,89,101,149,157,163,173,179,185,199,229,247,253,295,313,329,
%T A036952 331,355,367,379,383,405,425,443,453,457,471,523,533,539,565,583,587,
%U A036952 595,631,643,647,653,659,671,675,689,703,709,755,781,785,815,841,855
%N A036952 Primes p with property that the binary expansion of p is also a base-10 prime.
%e A036952 3 = 11_2 is OK because 11 is a prime.
%e A036952 5 = 101_2 is OK because 101 is a prime.
%e A036952 7 = 111_2 is not OK because 111 = 3*37.
%e A036952 11 = 1011_2 is not OK because 1011 = 3*337.
%e A036952 313 = 100111001_2 is OK because 100111001{10} is prime.

But as Gerald points out, 185 is not a prime.
So my interpretation can't be right.  In fact my interpretation leads to a
different entry:

%S A065720 3,5,23,47,89,101,149,157,163,173,179,199,229,313,331,367,379,383,443,
%T A065720 457,523,587,631,643,647,653,659,709,883,947,997,1009,1091,1097,1163,
%U A065720 1259,1277,1283,1289,1321,1483,1601,1669,1693,1709,1753,1877
%N A065720 Primes p such that the decimal expansion of its base 2 conversion is also prime.

Does anyone know what A036952 really is?  Richard Mathar mentions it here:

%S A156059 185,247,253,295,329,355,405,425,453,471,533,539,565,583,595,671,675,
%T A156059 689,703,755,781,785,815,841,855,925,989,1037,1075,1099,1113,1121,1159,
%U A156059 1189,1207,1219,1269,1287,1305,1329,1341,1403,1413,1441,1473,1521,1541
%N A156059 Composite & binary representation reads as decimal prime.
%C A156059 Subsequence of A036952. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb \
10 2009]
%e A156059 185 is composite & 10111001 is prime.

Neil

```