A331663 Odd composite numbers k with at least one divisor that is not a binary palindrome (A006995) such that the divisors of the binary reversal of k (A030101) are the binary reversals of the divisors of k.

95, 111, 123, 125, 187, 221, 335, 485, 597, 629, 655, 681, 697, 831, 965, 1011, 1139, 1389, 1461, 1535, 1563, 1649, 1731, 1791, 1983, 2031, 2043, 2045, 2227, 2493, 2605, 2733, 2827, 2885, 2901, 3033, 3099, 3279, 3281, 3327, 3341, 3459, 3647, 3891, 4039, 4083

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

95 is a term since the binary representations of its divisors, 1, 5, 19, and 95, are 1, 101, 10011 and 1011111, and their binary reversals, 1, 101, 11001 and 1111101, or  1, 5, 25 and 125 in decimal representation, are the divisors of 125, which is the binary reversal of 95, and 19 and 95 are not binary palindromes.

Mathematica

binPalQ[n_] := PalindromeQ @ IntegerDigits[n, 2]; Select[Range[1, 4000, 2], CompositeQ[#] && (Divisors @ IntegerReverse[#, 2]) == IntegerReverse[(d = Divisors[#]), 2] && !AllTrue[Rest[d], binPalQ] &]

Crossrefs

Cf. A006995, A030101.

Complement of A329419 with respect to A331662.

A331664 is a subsequence.

Sequence in context: A338581 A306303 A181767 * A046005 A339522 A045121

Adjacent sequences: A331660 A331661 A331662 * A331664 A331665 A331666

Keyword

nonn,base

Author

Amiram Eldar, Jan 23 2020

Status

approved