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A330999
Infinitary Ruth-Aaron numbers: numbers k such that A181894(k) = A181894(k+1).
3
5, 77, 714, 948, 2431, 2491, 2996, 3450, 4293, 5405, 5560, 5885, 5959, 11124, 13869, 14587, 16932, 17080, 17346, 18468, 19551, 26642, 31931, 33019, 37925, 42250, 47544, 48635, 49240, 52554, 53192, 60048, 79248, 80837, 89979, 95709, 98119, 98644, 99163, 108458
OFFSET
1,1
COMMENTS
A variation of Ruth-Aaron numbers with "Fermi-Dirac primes" (or infinitary components) instead of primes divisors.
LINKS
EXAMPLE
5 is a term since A181894(5) = A181894(6) = 5.
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 05 2020
STATUS
approved