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

Author

Amiram Eldar, Jan 13 2023

Keywords

• nonn

Comments

Are there 3 terms in A359747 that are consecutive integers?

Examples

			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).
		

Links

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

Crossrefs

Subsequence of A130091, A342028, A342029 and A359748.

Programs

Mathematica

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

PARI

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