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%I #7 Sep 08 2022 08:45:45
%S 7,11,13,17,19,23,29,31,37,37,41,43,47,47,53,53,59,61,67,71,71,73,79,
%T 83,89,89,97,97,101,101,103,107,109,113,127,131,137,137,139,149,149,
%U 151,157,163,163,167,167,173,179,179,181,193,191,193,197,199,211,223,227
%N Subsequence of A161986 consisting of all terms that are prime.
%C A161986(n) = k+r where k is n-th composite and r is remainder of (largest prime divisor of k) divided by (smallest prime divisor k).
%e A161986(1) to A161986(27) are 4, 7, 8, 9, 11, 13, 15, 17, 16, 19, 21, 22, 23, 25, 25, 27, 27, 29, 31, 32, 35, 35, 37, 37, 39, 40, 41. Hence a(1) to a(11) are the prime terms among them, namely 7, 11, 13, 17, 19, 23, 29, 31 ,37, 37, 41.
%o (Magma) [ p: n in [2..230] | not IsPrime(n) and IsPrime(p) where p is n+D[ #D] mod D[1] where D is PrimeDivisors(n) ];
%Y Cf. A161986 (A002808(n)+A161849(n)), A002808 (composite numbers), A161849 (A052369(n) mod A056608(n)), A052369 (largest prime factor of n-th composite), A056608 (smallest divisor of n-th composite).
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Jun 20 2009
%E Edited and corrected (a(19)=57 replaced by 67; a(38)=137, a(49)=179, a(50)=179 inserted) by _Klaus Brockhaus_, Jun 24 2009
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