A145195 Odd composite numbers n with property that at least one prime divisor p of n is a substring of the binary representation of n.

15, 27, 39, 45, 51, 55, 57, 63, 75, 85, 87, 91, 93, 95, 99, 105, 111, 117, 119, 123, 125, 135, 141, 147, 153, 155, 159, 165, 171, 175, 177, 183, 185, 187, 189, 195, 201, 205, 207, 213, 215, 219, 221, 225, 231, 235, 237, 243, 245, 247, 249, 255, 267, 279, 285

Offset

1,1

Comments

It is obvious that all even numbers and all prime numbers would meet this criterion.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Example

15 is 1111_2 and 15=3*5 where 3 is 11_2, so 15 is a term.

Mathematica

f[n_] := Block[{nb = ToString@ FromDigits@ IntegerDigits[n, 2], psb = ToString@ FromDigits@ IntegerDigits[ #, 2] & /@ First@ Transpose@ FactorInteger@n, c = 0, k = 1}, lmt = 1 + Length@ psb; While[k < lmt, If[ StringCount[nb, psb[[k]]] > 0, c++ ]; k++ ]; c]; f[1] = 0; Select[ Range@ 286, !PrimeQ@ # && OddQ@ # && f@# > 0 &]

Crossrefs

Cf. A014076, A143791.

Sequence in context: A307854 A053177 A349175 * A096022 A097222 A004069

Adjacent sequences: A145192 A145193 A145194 * A145196 A145197 A145198

Keyword

easy,nonn,base

Author

Robert G. Wilson v, Oct 03 2008

Status

approved