A235935 - OEIS

A235935

Primes p with f(p), f(f(p)), f(f(f(p))), f(f(f(f(p)))) all prime, where f(n) = prime(n) - n + 1.

2, 3, 2861, 8753, 56821, 83449, 162787, 165883, 167197, 186397, 217309, 261721, 275939, 309493, 355571, 382351, 467293, 501187, 539303, 560029, 602839, 640307, 657299, 708959, 879859, 919129, 973813, 1057741, 1085779, 1115899, 1156031, 1302667, 1366297, 1396427, 1516279, 1580461, 1760419, 1829797, 1867249, 1870021

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OFFSET

1,1

COMMENTS

By the general conjecture in A235925, this sequence should have infinitely many terms.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..100

Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

EXAMPLE

a(3) = 2861 with 2861, f(2861) = 23143, f(23143) = 240769 and f(240769) = 3117791 and f(3117791) = 48951967 all prime.

MATHEMATICA

f[n_]:=Prime[n]-n+1

p[k_]:=PrimeQ[f[Prime[k]]]&&PrimeQ[f[f[Prime[k]]]]&&PrimeQ[f[f[f[Prime[k]]]]]&&PrimeQ[f[f[f[f[Prime[k]]]]]]

n=0; Do[If[p[k], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 100000}]

CROSSREFS

Cf. A000040, A234695, A235925, A235934.

Sequence in context: A324310 A125612 A185156 * A182383 A257552 A038104

Adjacent sequences: A235932 A235933 A235934 * A235936 A235937 A235938

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 17 2014

STATUS

approved