

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
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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*pq 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



