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

1,1

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.

Links

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

Example

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

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;

Crossrefs

Cf. A022004, A341322.

Sequence in context: A094205 A136091 A184968 * A022004 A339503 A172454

Adjacent sequences: A341354 A341355 A341356 * A341358 A341359 A341360

Keyword

nonn

Author

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

Status

approved