A359748 Numbers k such that k and k+1 are both in A359747.

3, 7, 71, 107, 242, 431, 1151, 2591, 3887, 21599, 49391, 76831, 79999, 107647, 139967, 179999, 197567, 268911, 345599, 346111, 401407, 438047, 472391, 995327, 1031047, 1143071, 1249999, 1254527, 1349999, 1438207, 1685447, 2056751, 2411207, 2829887, 3269807, 4464071

Offset

1,1

Comments

Are there 3 terms in A359747 that are consecutive integers?

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

Example

7 is a term since 7*8 = 56 = 2^3 * 3^1 has 2 distinct exponents in its prime factorization (1 and 3) and 8*9 = 72 = 2^3 * 3^2 also has 2 distinct exponents in its prime factorization (2 and 3).

Mathematica

q[n_] := UnsameQ @@ (FactorInteger[n*(n+1)][[;; , 2]]); Select[Range[10^5], q[#] && q[#+1] &]

Prog

(PARI) is(n) = { my(e1 = factor(n*(n+1))[, 2], e2 = factor((n+1)*(n+2))[, 2]); #Set(e1) == #e1 && #Set(e2) == #e2; }

Crossrefs

Subsequence of A130091, A342028, A342029 and A359748.

Sequence in context: A127177 A261136 A127179 * A113841 A128072 A094008

Adjacent sequences: A359745 A359746 A359747 * A359749 A359750 A359751

Keyword

nonn

Author

Amiram Eldar, Jan 13 2023

Status

approved