OFFSET
1,1
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).
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.
EXAMPLE
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Aug 07 2022
STATUS
approved