%I #9 Apr 06 2020 02:20:23

%S 2,3,4,16,20,35,143,152,208,256,650,1624,2232,4233,4345,5368,8099,

%T 9424,11024,11919,12099,14905,18424,20220,21716,22194,24335,25592,

%U 26123,27390,30457,34945,38180,40425,51992,52206,52947,56563,63712,65536,67123,71154,71284

%N Numbers k such that A181894(k)+1 = A181894(k+1).

%C A variation of A064111 and A228126 with "Fermi-Dirac primes" (or infinitary components) instead of prime divisors.

%H Amiram Eldar, <a href="/A333802/b333802.txt">Table of n, a(n) for n = 1..10000</a>

%e 4 is a term since A181894(4) + 1 = 4 + 1 = 5 = A181894(5).

%t f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], 1])); s[1] = 0; s[n_] := Plus @@ (Flatten @ (f @@@ FactorInteger[n])); seq = {}; s1 = 0; Do[s2 = s[n]; If[s1 + 1 == s2, AppendTo[seq, n - 1]]; s1 = s2, {n, 2, 10^5}]; seq

%Y Cf. A006145, A039752, A050376, A064111, A181894, A228126, A330999, A333801.

%K nonn

%O 1,1

%A _Amiram Eldar_, Apr 05 2020