A356450 Positions of numbers m = A005940(n+1) such that m < n.

8, 16, 17, 32, 33, 34, 35, 64, 65, 66, 67, 68, 69, 71, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 139, 143, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 269, 271, 272, 273, 275, 279, 287, 288, 384, 512, 513, 514, 515, 516, 517, 518, 519, 520

Offset: 1

Author

Michael De Vlieger, Aug 07 2022

Keywords

• nonn

Comments

This sequence contains 2^k for k >= 3. Powers of 2 expressed in binary consist of a 1 followed by k zeros. Therefore, A005940(2^k) = prime(k+1)^1. For k >= 3, 2^k > prime(k+1).

Examples

			34 is in the sequence since A005940(34) = A005940("100010"_2) = prime(1+1)^1 * prime(4+1)^1 = 33, and 33 < 34.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..13175 (terms m < 2^21)
• Michael De Vlieger, Fan style binary tree diagram of b(n) for n = 1..2^14-1, where b(n) = A005940(n), highlighting terms such that b(n+1) < n in red, b(n+1) = n in yellow, and b(n+1) > n in blue. Positions of the terms shown in red are in this sequence, while b(A029747(n)+1) = A029747(n) appears in yellow.

Crossrefs

Cf. A005940, A029747, A356455.

Programs

Mathematica

nn = 2^10; a[0] = 1; Reap[Do[k = Prime[1 + DigitCount[n, 2, 0]]*a[n - 2^Floor@ Log2@ n]; Set[a[n], k]; If[k < n, Sow[n]], {n, nn}]][[-1, -1]] (* Michael De Vlieger, Aug 07 2022 *)