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%I #18 Jan 04 2025 16:30:18
%S 1,3,5,7,9,11,15,17,19,21,25,29,31,35,37,39,49,51,55,57,59,61,69,73,
%T 77,79,81,89,91,95,103,105,107,117,119,121,125,129,131,135,139,141,
%U 149,151,155,157,165,169,171,179,183,191,195,197,199,201,205,207,217,219,221,231,239
%N a(1)=1, then a(n) = least number > a(n-1) such that 2*a(n-1)+a(n) is prime.
%C I conjecture that any initial term a(1) eventually merges with this sequence.
%H Harvey P. Dale, <a href="/A256862/b256862.txt">Table of n, a(n) for n = 1..1000</a>
%t a=1;s={a};Do[x=a+1+Mod[a,2];While[!PrimeQ[2*a+x],x=x+2];s={s,x};a=x,{100}];s=Flatten[s]
%t lngp[n_]:=Module[{k=n+1},While[!PrimeQ[2n+k],k++];k]; NestList[lngp,1,70] (* _Harvey P. Dale_, Jan 04 2025 *)
%o (PARI) v=[1];n=2;while(#v<100,if(isprime(2*v[#v]+n),v=concat(v,n));n++);v \\ _Derek Orr_, Apr 14 2015
%K nonn,easy
%O 1,2
%A _Zak Seidov_, Apr 11 2015