A331000 -id:A331000 - cp's OEIS frontend

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

Amiram Eldar, Jan 05 2020

nonn

A variation of Ruth-Aaron numbers with "Fermi-Dirac primes" (or infinitary components) instead of prime divisors.

			5 is a term since A181894(5) = A181894(6) = 5.

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

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

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

A333801 Numbers k such that A008475(k)+1 = A008475(k+1).

Original entry on oeis.org

2, 3, 4, 7, 8, 16, 20, 31, 35, 127, 143, 208, 256, 650, 1479, 2464, 2623, 4233, 4345, 5183, 8099, 8191, 9424, 11024, 11919, 12099, 14905, 16159, 20220, 20800, 21716, 22194, 24335, 26123, 27335, 27390, 30457, 34945, 38180, 40425, 52206, 56563, 65536, 67123, 68264

Offset: 1

Amiram Eldar, Apr 05 2020

nonn

A variation of A064111 and A228126 with unitary prime-power divisors instead of prime divisors.

			4 is a term since A008475(4) + 1 = 4 + 1 = 5 = A008475(5).

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

Cf. A006145, A008475, A039752, A064111, A228126, A331000, A333802.

s[1] = 0; s[n_] := Plus @@ (Power @@@ FactorInteger[n]); seq = {}; s1 = 0; Do[s2 = s[n]; If[s1 + 1 == s2, AppendTo[seq, n - 1]]; s1 = s2, {n, 2, 10^5}]; seq

cp's OEIS Frontend

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

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