A346910 - OEIS

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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).

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

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OFFSET

1,1

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.

LINKS

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

EXAMPLE

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.

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

CROSSREFS

Cf. A066312, A141399.

Sequence in context: A354543 A324072 A327901 * A290560 A136017 A048628

Adjacent sequences: A346907 A346908 A346909 * A346911 A346912 A346913

KEYWORD

nonn

AUTHOR

Amiram Eldar, Aug 06 2021

STATUS

approved