A331662 -id:A331662 - cp's OEIS frontend

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

Amiram Eldar, Jan 23 2020

			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.

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

Cf. A006995, A030101.
Complement of A329419 with respect to A331662.
A331664 is a subsequence.

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

A331664 Odd composite numbers k all of whose divisors larger than 1 are not binary palindromes (A006995) such that the divisors of the binary reversal of k (A030101) are the binary reversals of the divisors of k.

Original entry on oeis.org

4847, 5371, 7141, 7913, 22891, 23243, 27053, 27469, 47863, 48599, 60349, 61277, 69211, 73343, 77251, 80623, 81863, 89339, 100201, 111841, 114293, 116729, 126649, 130289, 138623, 180163, 200693, 260833, 286141, 319381, 348121, 371899, 383339, 388561, 439517, 453037

Offset: 1

Amiram Eldar, Jan 23 2020

			4847 is a term since the binary representations of its divisors, 1, 37, 131 and 4847, are 1, 100101, 10000011 and 1001011101111, and their binary reversals, 1, 101001, 11000001 and 1111011101001, or 1, 41, 193 and 7913 in decimal representation, are the divisors of 7913, and none of the divisors of 4847 except 1 are binary palindromes.

Amiram Eldar, Table of n, a(n) for n = 1..2000

Cf. A006995, A030101, A329419.

Subsequence of A331662 and A331663.

binPalQ[n_] := PalindromeQ @ IntegerDigits[n, 2]; Select[Range[1, 5*10^5, 2], CompositeQ[#] && (Divisors@IntegerReverse[#, 2]) == IntegerReverse[(d = Divisors[#]), 2] && !AnyTrue[Rest[d], binPalQ] &]

cp's OEIS Frontend

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.

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