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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
By the general conjecture in A235925, this sequence should have infinitely many terms.
LINKS
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
Sequence in context: A324310 A125612 A185156 * A182383 A257552 A038104
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jan 17 2014
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)