

A342572


Positive numbers all of whose prime factors are binary palindromes.


1



1, 3, 5, 7, 9, 15, 17, 21, 25, 27, 31, 35, 45, 49, 51, 63, 73, 75, 81, 85, 93, 105, 107, 119, 125, 127, 135, 147, 153, 155, 175, 189, 217, 219, 225, 243, 245, 255, 257, 279, 289, 313, 315, 321, 343, 357, 365, 375, 381, 405, 425, 441, 443, 459, 465, 511, 525, 527
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OFFSET

1,2


LINKS



FORMULA

Sum_{n>=1} 1/a(n) = Product_{p in A016041} p/(p1) = 2.52136...


EXAMPLE

15 is a term since the binary representation of its prime factors, 3 and 5, are both palindromes: 11 and 101.
1 is a term because it has no prime factors, and "the empty set has every property".  N. J. A. Sloane, Jan 16 2022


MATHEMATICA

seq[max_] := Module[{ps = Select[Range[max], PalindromeQ @ IntegerDigits[#, 2] && PrimeQ[#] &], s = {1}, s1, s2}, Do[p = ps[[k]]; emax = Floor@Log[p, max]; s1 = Join[{1}, p^Range[emax]]; s2 = Select[Union[Flatten[Outer[Times, s, s1]]], # <= max &]; s = Union[s, s2], {k, 1, Length[ps]}]; s]; seq[1000]
Join[{1}, Module[{bps=Select[Prime[Range[200]], IntegerDigits[#, 2] == Reverse[ IntegerDigits[ #, 2]]&]}, Select[ Range[Max[ bps]], SubsetQ[ bps, FactorInteger[#][[All, 1]]]&]]] (* Harvey P. Dale, Jan 16 2022 *)


PROG

(Python)
from sympy import factorint
def ispal(s): return s == s[::1]
def ok(n): return n > 0 and all(ispal(bin(f)[2:]) for f in factorint(n))


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



