

A162722


A positive integer n is included if when n is represented in binary, it contains the binary representations of every distinct prime dividing n as substrings, with overlapping of the substrings allowed (but not necessary).


1



2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 24, 26, 27, 28, 29, 31, 32, 34, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 52, 53, 54, 55, 56, 58, 59, 61, 62, 63, 64, 67, 68, 71, 73, 74, 75, 76, 79, 80, 82, 83, 86, 88, 89, 90, 92, 94, 96, 97, 101, 103, 104, 106, 107
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OFFSET

1,1


COMMENTS

Every integer of the form p*2^k, p = prime, k>=0, is in this sequence. Every integer of the form p*2^k, p = odd prime, is missing from sequence A162721.


LINKS

Table of n, a(n) for n=1..71.


EXAMPLE

20 in binary is 10100. The distinct primes dividing 20 are 2 and 5, which are 10 and 101 in binary. Both 10 and 101 occur in 10100 (with overlapping). So 20 is in this sequence.


CROSSREFS

A162721, A123345
Sequence in context: A324935 A328369 A207674 * A123345 A093641 A209638
Adjacent sequences: A162719 A162720 A162721 * A162723 A162724 A162725


KEYWORD

base,nonn


AUTHOR

Leroy Quet, Jul 11 2009


EXTENSIONS

Corrected and extended by Sean A. Irvine, Dec 14 2009


STATUS

approved



