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A162722
A positive integer k is included if when k is represented in binary, it contains the binary representations of every distinct prime dividing k as substrings, with overlapping of the substrings allowed (but not necessary).
2
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
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
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.
MATHEMATICA
q[n_] := AllTrue[FactorInteger[n][[;; , 1]], StringContainsQ[IntegerString[n, 2], IntegerString[#, 2]] &]; Select[Range[2, 100], q] (* Amiram Eldar, Nov 10 2021 *)
CROSSREFS
Sequence in context: A324935 A328369 A207674 * A123345 A093641 A209638
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Jul 11 2009
EXTENSIONS
Corrected and extended by Sean A. Irvine, Dec 14 2009
STATUS
approved