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%I #9 Sep 25 2019 11:27:38
%S 2,503,709,907,911,1109,2729,2927,3739,4139,4547,5351,5557,6361,6971,
%T 7573,7577,8179,10607,11411,11617,12421,12829,13229,14243,15451,15859,
%U 16057,16061,17471,19697,21107,21313,21713,22727,23531,26161,26561
%N a(n) = smallest prime > a(n-1) such that a(n)+a(n-1) is multiple of k, a(1)=2, k=101.
%H Harvey P. Dale, <a href="/A178468/b178468.txt">Table of n, a(n) for n = 1..1000</a>
%e 2+503=505=5*101, 503+709=1212=12*101, 709+907=1616=16*101.
%t k=101; a=p=2; s={2}; Do[p=NextPrime[p]; If[Mod[a+p, k]==0, a=p; AppendTo[s, a]], {10000}]; s
%t sp[n_]:=Module[{p=NextPrime[n]},While[Mod[n+p,101]!=0,p=NextPrime[p]];p]; NestList[sp,2,40] (* _Harvey P. Dale_, Sep 25 2019 *)
%Y Cf. A178429 - A178467 cases k=23(2)99, A175442 - A175451 cases k=3(2)21.
%K nonn
%O 1,1
%A _Zak Seidov_, May 28 2010