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A341357
Primes p such that q*r == p (mod q+r) where q and r are the next primes after p.
1
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
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
Sequence in context: A094205 A136091 A184968 * A022004 A339503 A172454
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Feb 09 2021
STATUS
approved