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a(1)=1. a(n) = number of earlier terms of the sequence which when added to n produce a composite number.
4

%I #15 Sep 07 2017 02:42:29

%S 1,0,1,1,3,2,5,5,7,4,8,5,10,9,11,10,14,10,13,16,14,16,18,18,19,20,16,

%T 20,21,23,23,25,23,27,30,23,27,27,31,27,33,31,31,33,37,31,41,31,41,39,

%U 40,34,43,45,47,36,45,40,50,43,51,44,47,50,56,41,56,53,55,47,61,55,60,57

%N a(1)=1. a(n) = number of earlier terms of the sequence which when added to n produce a composite number.

%H G. C. Greubel, <a href="/A115207/b115207.txt">Table of n, a(n) for n = 1..10000</a>

%e Adding 7 to the first 6 terms of the sequence gives [8,7,8,8,10,9]. Of these terms, five are composite, so a(7) = 5.

%t a = {1, 0}; For[n = 3, n < 10001, n++, in = 0; For[j = 1, j < Length[a] + 1, j++, If[! PrimeQ[n + a[[j]]], in++]]; AppendTo[a, in]]; a (* _G. C. Greubel_, Feb 05 2016 *)

%o (PARI) seq=vector(200); seq[1]=1; print1(1,","); for(j=1,190,count=0; for(k=1,j,if(isprime(j+1+seq[k])==0 && (j+1+seq[k])>1,count=count+1;)); seq[j+1]=count; print1(seq[j+1],",")) \\ _Matthew Conroy_, Feb 09 2006

%Y Cf. A115208, A115209, A115210.

%K nonn

%O 1,5

%A _Leroy Quet_, Jan 16 2006

%E More terms from _Matthew Conroy_, Feb 09 2006