OFFSET
1,1
COMMENTS
Numbers k such that k and k+1 are both terms of A283050.
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 1, 8, 82, 802, 8009, 80078, 800900, 8009533, 80097354, 800979764, 8009809838, ... . Apparently, the asymptotic density of this sequence exists and equals 0.08009... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
8 is a term since 2 is the least prime factor of 8 and 8 is divisible by 2^2 = 4, and 3 is the least prime factor of 9 and 9 is divisible by 3^3 = 9.
MATHEMATICA
q[n_] := FactorInteger[n][[1, -1]] >= 2; consec[kmax_] := Module[{m = 1, c = Table[False, {2}], s = {}}, Do[c = Join[Rest[c], {q[k]}]; If[And @@ c, AppendTo[s, k - 1]], {k, 1, kmax}]; s]; consec[640]
PROG
(PARI) lista(kmax) = {my(q1 = 0, q2); for(k = 2, kmax, q2 = factor(k)[1, 2] >= 2; if(q1 && q2, print1(k-1, ", ")); q1 = q2); }
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 21 2023
STATUS
approved