A255694 Primes p such that five iterations of the map p->2p+nextprime(p) give primes.

1538419, 3662941, 10835789, 11698837, 13441633, 16002521, 19039199, 28598753, 29170307, 57766903, 58309837, 60324577, 71197453, 75817459, 84834049, 86506051, 127779919, 130415413, 184465669, 189978779, 221705713, 230700227, 231203779, 239519327, 255285439

Offset: 1

Author

Zak Seidov, Mar 15 2015

Keywords

• nonn

Comments

Apparently there is no limit for number of iterations of the map p->2p+nextprime(p) all giving primes.

E.g., first primes with 6 iterations all giving primes are 1854811727,1988791547,2498711497,2866433161,3337303943,3514209079.

Examples

			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.
		

Crossrefs

Subsequence of A173971. Cf. A151800.

Programs

Mathematica

fimQ[p_]:=AllTrue[NestList[2#+NextPrime[#]&,p,5],PrimeQ]; Select[Prime[Range[ 13960000]],fimQ] (* Harvey P. Dale, Oct 09 2023 *)