A341357 Primes p such that q*r == p (mod q+r) where q and r are the next primes after p.

5, 11, 17, 41, 101, 107, 191, 227, 311, 347, 461, 467, 641, 821, 857, 881, 1091, 1277, 1301, 1427, 1481, 1487, 1511, 1607, 1811, 1871, 1997, 2081, 2237, 2267, 2447, 2657, 2687, 3251, 3461, 3527, 3671, 3917, 4001, 4127, 4517, 4637, 4787, 4931, 4967, 5039, 5231, 5477, 5501, 5651, 6101, 6197, 6827

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 09 2021

Keywords

• nonn

Comments

If for some k >= 0 we have q=p+2*(k+1)*(2*k+1) and r=p+2*(k+1)*(2*k+3) then p is in the sequence. This includes A022004 in the case k=0.

It appears that all terms are of the above form.

Examples

			a(3) = 17 is in the sequence because with p = 17, q = 19, r = 23, q*r = 437 == 17 (mod 19+23=42).
		

Links

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

Crossrefs

Cf. A022004, A341322.

Programs

Maple

q:= 2: r:= 3: count:= 0: R:= NULL:
while count < 100 do
  p:= q: q:= r: r:= nextprime(r);
if (q*r) mod (q+r) = p then count:= count+1; R:= R, p fi;
od:
R;