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

1,4

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.

Links

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

Example

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.

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] ]

Crossrefs

Cf. A354790, A356803.

Sequence in context: A001970 A006951 A224840 * A345334 A354294 A132891

Adjacent sequences: A356801 A356802 A356803 * A356805 A356806 A356807

Keyword

nonn,base

Author

Michael De Vlieger, Sep 06 2022

Status

approved