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%I #11 Jan 06 2020 08:37:02
%S 5,77,714,948,2431,2491,2996,3450,4293,5405,5560,5885,5959,11124,
%T 13869,14587,16932,17080,17346,18468,19551,26642,31931,33019,37925,
%U 42250,47544,48635,49240,52554,53192,60048,79248,80837,89979,95709,98119,98644,99163,108458
%N Infinitary Ruth-Aaron numbers: numbers k such that A181894(k) = A181894(k+1).
%C A variation of Ruth-Aaron numbers with "Fermi-Dirac primes" (or infinitary components) instead of primes divisors.
%H Amiram Eldar, <a href="/A330999/b330999.txt">Table of n, a(n) for n = 1..10000</a>
%e 5 is a term since A181894(5) = A181894(6) = 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 == s2, AppendTo[seq, n-1]]; s1 = s2, {n, 2, 10^5}]; seq
%Y Cf. A006145, A039752, A050376, A181894, A331000.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jan 05 2020
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