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A339691 a(n) is the least prime p > prime(n+1) such that p == -prime(n+1) (mod prime(n)). 1
5, 7, 13, 17, 31, 61, 83, 53, 109, 317, 149, 107, 367, 211, 229, 577, 293, 421, 197, 211, 359, 233, 409, 971, 1063, 503, 1129, 2459, 541, 1229, 631, 911, 409, 2909, 743, 1051, 1093, 811, 829, 859, 1609, 1619, 571, 1733, 983, 983, 2309, 2003, 6581, 683, 2557, 1193, 5051, 1249, 1279, 2887, 2957 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) >= 4*prime(n)-prime(n+1), with equality when prime(n) is in A227907.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

For n=5 we have prime(5)=11 and prime(6)=13, and a(5)=31 because of the numbers == -13 (mod 11) and greater than 13 (20, 31, ...), 31 is the first prime.

MAPLE

f:= proc(n) local p, q, r0, r;

  p:= ithprime(n);

  q:= nextprime(p);

  for r from 4*p-q by p do if isprime(r) then return r fi od;

end proc:

map(f, [$1..100]);

PROG

(PARI) a(n) = my(p=prime(n+2)); while(Mod(p, prime(n)) != -prime(n+1), p = nextprime(p+1)); p; \\ Michel Marcus, Dec 13 2020

CROSSREFS

Cf. A227907.

Sequence in context: A172480 A285886 A106069 * A076294 A073574 A092110

Adjacent sequences:  A339688 A339689 A339690 * A339692 A339693 A339694

KEYWORD

nonn,look

AUTHOR

J. M. Bergot and Robert Israel, Dec 13 2020

STATUS

approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)