cp's OEIS Frontend

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

%I A343133 #8 Jul 08 2021 06:48:06
%S A343133 1,9,58,61,73,80,82,1224,1368,3075,3720,5328,22112,45890,145132,
%T A343133 145138,269843,377739,399281,622515,744768,1280073,1280437,1280441,
%U A343133 1281165,1281190,1281241,2961840,33275384,54025424,54161775,70695344,91136415,922135875,922141772
%N A343133 Numbers k such that A064839(k) = A064839(k+1).
%C A343133 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, ...
%C A343133 Are there numbers k such that A064839(k) = A064839(k+1) = A064839(k+2)?
%e A343133 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.
%e A343133 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.
%t A343133 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
%Y A343133 Cf. A025487, A064839.
%Y A343133 Cf. A001248, A006881.
%K A343133 nonn
%O A343133 1,2
%A A343133 _Amiram Eldar_, Jul 07 2021