# [seqfan] Re: Binary Primes In Binary Primes

Douglas McNeil mcneil at hku.hk
Tue Mar 16 07:50:15 CET 2010

```I think something's gone wrong: 479 is listed twice.

I can verify your hand-calculated terms.  I calculate
> 2, 5, 11, 3, 7, 23, 47, 191, 31, 127, 383, 3067, 13, 29, 59, 239, 479,
> 223, 479, 991, 61, 251, 503, 2039, 509, 1019, 2039, 4079, 16319,
>

sage: a[:100]
[2, 5, 11, 3, 7, 23, 47, 191, 31, 127, 383, 3067, 13, 29, 59, 239, 479, 223,
991, 61, 251, 503, 2039, 509, 1019, 4079, 16319, 65407, 1021, 4091, 24571,
4093, 16381, 98299, 6143, 63487, 3583, 15359, 129023, 3967, 16127, 98047,
1531, 7159, 1789, 7933, 24317, 379, 1783, 5879, 367, 1471, 7039, 109, 439,
1759, 18143, 17, 71, 199, 797, 3191, 571, 2287, 9151, 36607, 429823, 163,
419, 839, 2887, 6983, 3491, 13967, 55871, 3359, 6719, 26879, 1151, 9209,
73673, 73, 293, 37, 101, 229, 919, 151, 607, 4703, 587, 2351, 14639, 457,
1481, 2963, 19, 79, 317, 829]

as the first hundred terms, and

sage: missing = [x for x in primes(1000) if x not in a]
sage: missing[:100]
[131, 193, 257, 263, 389, 449, 521, 523, 541, 547, 577, 641, 643, 673, 769,
773]

as the first few primes not found up to n=10000.  67, 97, and 113 seem to
appear at indices 9637, 9642, and 222 (zero-indexed, as God intended).

Usual warnings about coffee-free programming apply..

Doug

--
Department of Earth Sciences
University of Hong Kong

```