OFFSET
1,1
COMMENTS
The conjecture in A260753 implies that the current sequence has infinitely many terms.
REFERENCES
Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28 - Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014.
EXAMPLE
a(1) = 3 since prime(3)-3+1 = 5-3+1 = prime(2) with 3 and 2 both prime.
a(3) = 71 since prime(71)-71+1 = 353-70 = 283 = prime(61) with 71 and 61 both prime.
MATHEMATICA
f[n_]:=Prime[Prime[n]]-Prime[n]+1
PQ[p_]:=PrimeQ[p]&&PrimeQ[PrimePi[p]]
n=0; Do[If[PQ[f[k]], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 1241}]
prQ[x_]:=Module[{c=Prime[x]-x+1}, AllTrue[{c, PrimePi[c]}, PrimeQ]]; Select[Prime[ Range[ 2000]], prQ] (* Harvey P. Dale, Apr 27 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Aug 18 2015
STATUS
approved