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

%I A346910 #10 Aug 21 2023 12:01:23
%S A346910 35,143,323,384,539,899,2430,3599,4199,4374,5183,11663,22499,32399,
%T A346910 36863,57599,72899,176399,186623,359999,656099,1102499,1327103,
%U A346910 2624399,5336099,6718463,8999999,11289599,16402499,23039999,34574399,39689999,54022499,57153599,77792399
%N A346910 Numbers k such that k and k+1 are both nonprime-powers whose all distinct prime divisors are consecutive primes (A066312).
%C A346910 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.
%H A346910 David A. Corneth, <a href="/A346910/b346910.txt">Table of n, a(n) for n = 1..741</a> (terms <= 10^20)
%e A346910 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.
%t A346910 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
%Y A346910 Cf. A066312, A141399.
%K A346910 nonn
%O A346910 1,1
%A A346910 _Amiram Eldar_, Aug 06 2021