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A179295
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a(n) is the least prime number such that prime(n)+a(n)+1 is a prime or -1 if no such prime number exists.
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1
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2, 3, 5, 3, 5, 3, 5, 3, 5, 7, 5, 3, 5, 3, 5, 5, 7, 5, 3, 7, 5, 3, 5, 7, 3, 5, 3, 5, 3, 13, 3, 5, 11, 11, 7, 5, 5, 3, 5, 5, 11, 11, 5, 3, 13, 11, 11, 3, 5, 3, 5, 11, 29, 5, 5, 5, 7, 5, 3, 11, 23, 13, 3, 5, 3, 13, 5, 11, 5, 3, 5, 7, 5, 5, 3, 5, 7, 3, 7, 11, 11
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OFFSET
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1,1
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COMMENTS
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If Maillet's conjecture is true, then a(n) != -1 for all n. - Chai Wah Wu, Aug 01 2017
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LINKS
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E. Maillet, Réponse, L’intermédiaire des math. 12 (1905), p. 108.
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EXAMPLE
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a(1) = 2, since prime(1) + 2 + 1 = 5.
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MATHEMATICA
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Table[Block[{p=2}, While[!PrimeQ[Prime[n] + p + 1], p=NextPrime[p]]; p], {n, 100}] (* Indranil Ghosh, Jun 30 2017 *)
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PROG
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(ANS Forth)
\ https://github.com/Lehs/ANS-Forth-libraries
s" numbertheory.4th" included
: get_number \ p -- q
locals| p | 1
begin nextprime dup p + 1+ isprime
until ;
: list_numbers \ N --
locals| N | 1
begin nextprime dup
get_number cr .
dup N >
until ;
(PARI) a(n) = my(pn=prime(n), p=2); while(! isprime(pn+p+1), p = nextprime(p+1)); p; \\ Michel Marcus, Jun 30 2017
(Python)
from sympy import prime, isprime, nextprime
def a(n):
p=2
while not isprime(prime(n) + p + 1): p=nextprime(p)
return p
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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