A346910 Numbers k such that k and k+1 are both nonprime-powers whose all distinct prime divisors are consecutive primes (A066312).

35, 143, 323, 384, 539, 899, 2430, 3599, 4199, 4374, 5183, 11663, 22499, 32399, 36863, 57599, 72899, 176399, 186623, 359999, 656099, 1102499, 1327103, 2624399, 5336099, 6718463, 8999999, 11289599, 16402499, 23039999, 34574399, 39689999, 54022499, 57153599, 77792399

Offset: 1

Author

Amiram Eldar, Aug 06 2021

Keywords

• nonn

Comments

Terms k such that the distinct prime divisors of k*(k+1) are consecutive primes are 35, 384, 539, 4374, ... These are also terms of A141399.

Examples

			35 = 5 * 7 is a term since 5 and 7 are consecutive primes, 35 + 1 = 36 = 2^2 * 3^2 and 2 and 3 are also consecutive primes.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..741 (terms <= 10^20)

Crossrefs

Cf. A066312, A141399.

Programs

Mathematica

q[n_] := Module[{p = FactorInteger[n][[;; , 1]], np}, np = Length[p]; np > 1 && PrimePi[p[[-1]]] - PrimePi[p[[1]]] == np - 1]; s = {}; n = 1; q1 = q[1]; Do[q2 = q[n]; If[q1 && q2, AppendTo[s, n - 1]]; q1 = q2; n++, {10^5}]; s