A356804 a(n) is a binary encoded version of A356803(n).

0, 0, 1, 3, 6, 14, 28, 31, 59, 123, 243, 499, 995, 2019, 2028, 2045, 4061, 4095, 8127, 16319, 32575, 65343, 130623, 261695, 523327, 1047615, 2095167, 4192319, 8386611, 8386679, 16775270, 16775279, 33550447, 67104879, 134213709, 134213727, 268427359, 536862815

Offset: 1

Author

Michael De Vlieger, Sep 06 2022

Keywords

• nonn
• base

Comments

Let S(n) = list of forbidden primes for A354790(n); A356803(n) is the product of these primes. Then a(n) = Sum of 2^(i-1) over all prime(i) in S(n).

Conversely, if a(n) has binary expansion a(n) = Sum b(i)*2^i, b(i) = 0 or 1, then S(n) consists of {prime(i+1) such that b(i) = 1}. (After comment by N. J. A. Sloane at A354765)

Analogous to A354765.

Examples

			For n = 7 the forbidden primes are 5, 7, 11 = prime(3), prime(4) and prime(5). Their product is A356803(7) = 385. Then a(7) = 2^2 + 2^3 + 2^4 = 28.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..3405

Crossrefs

Cf. A354790, A356803.

Programs

Mathematica

Block[{s = Import["https://oeis.org/A354790/a354790.txt", "Data"][[1 ;; 25, -1]], m = 0}, Join[{0, 0}, Reap[Do[If[i > 1, m += Total[2^PrimePi@ FactorInteger[s[[i - 1]]][[All, 1]]]]; If[IntegerQ[#] && # > 0, m -= Total[2^PrimePi@ FactorInteger[s[[#]]][[All, 1]]]] &[(i - 1)/2]; Sow[m], {i, Length[s]}] ][[-1, -1, 3 ;; -1]]/2] ]