login
a(n) is a binary encoded version of A356803(n).
1

%I #9 Sep 08 2022 01:35:01

%S 0,0,1,3,6,14,28,31,59,123,243,499,995,2019,2028,2045,4061,4095,8127,

%T 16319,32575,65343,130623,261695,523327,1047615,2095167,4192319,

%U 8386611,8386679,16775270,16775279,33550447,67104879,134213709,134213727,268427359,536862815

%N a(n) is a binary encoded version of A356803(n).

%C 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).

%C 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)

%C Analogous to A354765.

%H Michael De Vlieger, <a href="/A356804/b356804.txt">Table of n, a(n) for n = 1..3405</a>

%e 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.

%t 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] ]

%Y Cf. A354790, A356803.

%K nonn,base

%O 1,4

%A _Michael De Vlieger_, Sep 06 2022