A355483 -id:A355483 - cp's OEIS frontend

A355482 a(1) = 2; for n > 1, a(n) is the smallest positive number that has not yet appeared such that the number of 1-bits in the binary expansion of a(n) equals the number of proper divisors of a(n-1).

2, 4, 3, 8, 7, 16, 15, 11, 32, 31, 64, 63, 47, 128, 127, 256, 255, 191, 512, 511, 13, 1024, 1023, 223, 2048, 2047, 14, 19, 4096, 4095, 8388607, 21, 22, 25, 5, 8192, 8191, 16384, 16383, 239, 32768, 32767, 247, 26, 28, 55, 35, 37, 65536, 65535, 49151, 38, 41, 131072, 131071, 262144, 262143

Offset: 1

Scott R. Shannon, Jul 03 2022

This sequence is similar to A355374 but the rules for determining a(n) are reversed. The only fixed point in the first 145 terms is a(3) = 3. It is unknown if all numbers eventually appear. The last known term is a(145) which is a 154 digit number whose complete factorization is unknown.

			a(7) = 15 = 1111_2 as a(6) = 16 which has four proper divisors, and 15 is the smallest unused number that has four 1-bits in its binary expansion.

Scott R. Shannon, Table of n, a(n) for n = 1..145

Cf. A355483 (all divisors), A355374, A000120, A032741, A005179, A027751.

cp's OEIS Frontend

A355482 a(1) = 2; for n > 1, a(n) is the smallest positive number that has not yet appeared such that the number of 1-bits in the binary expansion of a(n) equals the number of proper divisors of a(n-1).

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