A343133 Numbers k such that A064839(k) = A064839(k+1).

1, 9, 58, 61, 73, 80, 82, 1224, 1368, 3075, 3720, 5328, 22112, 45890, 145132, 145138, 269843, 377739, 399281, 622515, 744768, 1280073, 1280437, 1280441, 1281165, 1281190, 1281241, 2961840, 33275384, 54025424, 54161775, 70695344, 91136415, 922135875, 922141772

Offset: 1

Author

Amiram Eldar, Jul 07 2021

Keywords

• nonn

Comments

The corresponding values of A064839 are 1, 2, 17, 18, 21, 2, 23, 10, 12, 278, 18, 21, 150, 2842, 13434, 13435, 13547, 3654, 33805, 55229, 150, 265608, 265682, 265683, 265832, 265837, 265849, 268, 773172, 308093, 308810, 395158, 540683, 24172493, 24172646, ...

Are there numbers k such that A064839(k) = A064839(k+1) = A064839(k+2)?

Examples

			9 is a term since 9 = 3^2 = A001248(2) is the second square of a prime, and 9 + 1 = 10 = 2 * 5 = A006881(2) is the second squarefree semiprime.
58 is a term since 58 = 2*29 = A001248(17) is the 17th squarefree semiprime, and 58 + 1 = 59 = A000040(17) is the 17th prime.
		

Crossrefs

Cf. A025487, A064839.

Cf. A001248, A006881.

Programs

Mathematica

lpsv = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]]; lps[n_] := Module[{s = Sort[FactorInteger[n][[;; , 2]]], m}, m = Length[s]; Product[Prime[i]^s[[m - i + 1]], {i, 1, m}]]; n = 100; mx = lpsv[[n]]; c = Table[0, {n}]; v1 = 1; s = {}; Do[lps1 = lps[k]; p = Position[lpsv, lps1][[1, 1]]; c[[p]]++; v2 = c[[p]]; If[v1 == v2, AppendTo[s, k - 1]]; v1 = v2, {k, 2, mx}]; s