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a(n) = 3*prime(n) - prime(n+1) - 3.
3

%I #18 Jan 31 2023 14:18:57

%S 0,1,5,7,17,19,29,31,37,53,53,67,77,79,85,97,113,113,127,137,137,151,

%T 157,167,187,197,199,209,211,209,247,253,269,265,293,293,305,319,325,

%U 337,353,349,377,379,389,383,407,439,449,451,457,473,469,493,505,517,533,533,547

%N a(n) = 3*prime(n) - prime(n+1) - 3.

%C Except for the initial term, a(n)==(1,5) mod 6.

%H Harvey P. Dale, <a href="/A100021/b100021.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A098764(n) - 3.

%p f:=n->3*ithprime(n)-ithprime(n+1)-3;

%t 3#[[1]]-#[[2]]-3&/@Partition[Prime[Range[80]],2,1] (* _Harvey P. Dale_, Oct 13 2018 *)

%o (PARI) a(n) = 3*prime(n) - prime(n+1) - 3; \\ _Michel Marcus_, Jan 31 2023

%Y Cf. A099389 for the primes arising in the sequence, A098764.

%K nonn,less

%O 1,3

%A _Giovanni Teofilatto_, Nov 20 2004

%E Corrected by Neven Juric (neven.juric(AT)apis-it.hr), rechecked by _N. J. A. Sloane_, Jun 13 2006