A330999 Infinitary Ruth-Aaron numbers: numbers k such that A181894(k) = A181894(k+1).

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A006145, A039752, A050376, A181894, A331000.

Sequence in context: A028556 A364713 A214867 * A331000 A039753 A277533

Adjacent sequences: A330996 A330997 A330998 * A331000 A331001 A331002

Keyword

nonn

Author

Amiram Eldar, Jan 05 2020

Status

approved