OFFSET
1,1
COMMENTS
Numbers k such that k and k+1 are both terms of A365869.
The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 5, 42, 414, 4173, 41927, 419597, 4196917, 41972747, 419738185, 4197406018, ... . Apparently, the asymptotic density of this sequence exists and equals 0.04197... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
44 is a term since the exponent of the prime factor 2 in the factorization 44 = 2^2 * 11 is 2, which is even, and the exponent of the prime factor 3 in the factorization 45 = 3^2 * 5 is also 2, which is even.
MATHEMATICA
q[n_] := EvenQ[FactorInteger[n][[1, -1]]]; 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[1250]
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