

A340431


Primes p such that, with q the next prime after p, q > p+2 and q^p == q (mod p+q) and p^q == p (mod p+q).


0



13, 211, 421, 523, 154321, 221941, 1556641, 2377201, 3918757, 4359961, 7842511, 9163873, 20446561, 1501102081, 7578849037, 15724210681, 25522638481, 52966796353, 68999668237, 109926997057, 112417709113, 209826685297, 694503347201, 963374692897
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OFFSET

1,1


COMMENTS

For twin primes p,q we always have p^q == p (mod p+q) and q^p == q (mod p+q).


LINKS

Table of n, a(n) for n=1..24.


EXAMPLE

a(3) = 421 is a term because the next prime is 431, 421^431 == 421 (mod 852) and 431^421 == 431 (mod 852).


MAPLE

q:= 2: R:= NULL:
while p < 10^7 do
p:= q; q:= nextprime(p);
if qp = 2 then next fi;
if q &^ p mod (p+q) = q and p &^ q mod (p+q) = p then
R:= R, p;
fi;
od:
R;


PROG

(Python)
from sympy import nextprime
A340431_list , p = [], 2
while p <= 10**10:
q = nextprime(p)
if q > p+2:
pq = p+q
if pow(q, p, pq) == q and pow(p, q, pq) == p:
A340431_list.append(p)
p = q # Chai Wah Wu, Jan 12 2021
(PARI) upto(n) = my(p=2); forprime(q = nextprime(p+1), n, if(qp > 2, if(Mod(p, p+q)^q == p, if(Mod(q, p+q)^p == q, print1(p, ", ")))); p = q); \\ Daniel Suteu, Jan 12 2021


CROSSREFS

Sequence in context: A145270 A296671 A196328 * A251093 A132542 A069989
Adjacent sequences: A340428 A340429 A340430 * A340432 A340433 A340434


KEYWORD

nonn,more


AUTHOR

J. M. Bergot and Robert Israel, Jan 12 2021


EXTENSIONS

a(15)a(17) from Daniel Suteu, Jan 12 2021
a(18)a(22) from Chai Wah Wu, Jan 15 2021
a(23)a(24) from Martin Ehrenstein, Jan 19 2021


STATUS

approved



