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a(n) is the smallest start of a run of 2 or more integers having a prime factor greater than n.
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%I #34 Mar 28 2023 07:59:43

%S 2,5,10,10,13,13,22,22,22,22,37,37,37,37,37,37,37,37,46,46,46,46,58,

%T 58,58,58,58,58,61,61,73,73,73,73,73,73,82,82,82,82,106,106,106,106,

%U 106,106,106,106,106,106,106,106,157,157,157,157,157,157,157,157,157,157,157,157,157,157,157

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

%C Each term is a prime or one less than a prime.

%C Each even term is twice an odd prime (except for a(1)=2).

%C Each prime term is of the form 2p-1 where p is prime.

%F Conjecture: a(n) ~ 2*n.

%e For n=5, a(5) = 13 since the two numbers 13 and 14=2*7 both have a prime factor > n.

%o (PARI) gpf(n) = vecmax(factor(n)[,1]); \\ A006530

%o a(n) = my(k=2); while(!((gpf(k)>n) && (gpf(k+1)>n)), k++); k; \\ _Michel Marcus_, Jan 10 2023

%Y Cf. A006530 (gpf), A359488 (run lengths).

%Y Cf. A327909.

%K nonn

%O 1,1

%A _Thomas Garrison_, Jan 02 2023