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

1,2

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)?

Links

Table of n, a(n) for n=1..35.

Example

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.

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

Crossrefs

Cf. A025487, A064839.

Cf. A001248, A006881.

Sequence in context: A112616 A197673 A012089 * A044147 A044528 A027174

Adjacent sequences: A343130 A343131 A343132 * A343134 A343135 A343136

Keyword

nonn

Author

Amiram Eldar, Jul 07 2021

Status

approved