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A359487 a(n) is the smallest start of a run of 2 or more integers having a prime factor greater than n.

%I A359487 #34 Mar 28 2023 07:59:43
%S A359487 2,5,10,10,13,13,22,22,22,22,37,37,37,37,37,37,37,37,46,46,46,46,58,
%T A359487 58,58,58,58,58,61,61,73,73,73,73,73,73,82,82,82,82,106,106,106,106,
%U A359487 106,106,106,106,106,106,106,106,157,157,157,157,157,157,157,157,157,157,157,157,157,157,157
%N A359487 a(n) is the smallest start of a run of 2 or more integers having a prime factor greater than n.
%C A359487 Each term is a prime or one less than a prime.
%C A359487 Each even term is twice an odd prime (except for a(1)=2).
%C A359487 Each prime term is of the form 2p-1 where p is prime.
%F A359487 Conjecture: a(n) ~ 2*n.
%e A359487 For n=5, a(5) = 13 since the two numbers 13 and 14=2*7 both have a prime factor > n.
%o A359487 (PARI) gpf(n) = vecmax(factor(n)[,1]); \\ A006530
%o A359487 a(n) = my(k=2); while(!((gpf(k)>n) && (gpf(k+1)>n)), k++); k; \\ _Michel Marcus_, Jan 10 2023
%Y A359487 Cf. A006530 (gpf), A359488 (run lengths).
%Y A359487 Cf. A327909.
%K A359487 nonn
%O A359487 1,1
%A A359487 _Thomas Garrison_, Jan 02 2023