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%I #29 Oct 09 2023 18:10:19
%S 1538419,3662941,10835789,11698837,13441633,16002521,19039199,
%T 28598753,29170307,57766903,58309837,60324577,71197453,75817459,
%U 84834049,86506051,127779919,130415413,184465669,189978779,221705713,230700227,231203779,239519327,255285439
%N Primes p such that five iterations of the map p->2p+nextprime(p) give primes.
%C Apparently there is no limit for number of iterations of the map p->2p+nextprime(p) all giving primes.
%C E.g., first primes with 6 iterations all giving primes are 1854811727,1988791547,2498711497,2866433161,3337303943,3514209079.
%e p=1538419, q=2p+np(p)=4615267, r=2q+np(q)=13845817, s=2r+np(r)=41537491, t=2s+np(s)=124612483, u=2t+np(t)=373837459 all prime, while v=2u+np(u)=1121512407=3*23*89*182627 is not prime; here np(m) = A151800(m) = next prime after m.
%t fimQ[p_]:=AllTrue[NestList[2#+NextPrime[#]&,p,5],PrimeQ]; Select[Prime[Range[ 13960000]],fimQ] (* _Harvey P. Dale_, Oct 09 2023 *)
%Y Subsequence of A173971. Cf. A151800.
%K nonn
%O 1,1
%A _Zak Seidov_, Mar 15 2015