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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).
1
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
1,1
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
Sequence in context: A354543 A324072 A327901 * A290560 A136017 A048628
KEYWORD
nonn
AUTHOR
Amiram Eldar, Aug 06 2021
STATUS
approved