A129191 Balanced primes p of the form (r+q+s-1)/2, where r, q, s are consecutive primes.

593, 1907, 4409, 6323, 15313, 17483, 19577, 25673, 26693, 29269, 34673, 38867, 46889, 54773, 64013, 67169, 68483, 74567, 81749, 85049, 95273, 96431, 110813, 111863, 127643, 132929, 134213, 134639, 135089, 140351, 156241, 157253, 160403

Offset

1,1

Comments

The primes q arising here are in A129190.

q need not be a balanced prime, see however A129242.

Links

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

Example

1907 = (1259+1277+1279-1)/2 is prime and 1259, 1277, 1279 are consecutive primes. 1907 = A006562(24) is a balanced prime, it has distance 6 to the preceding prime 1901 and to the next prime 1913. Hence 1907 is a term.

Maple

p:= 2: q:= 3: r:= 5:
Res:= NULL: count:= 0:
while count < 100 do
  p:= q; q:= r; r:= nextprime(r);
  s:= (p+q+r-1)/2;
  if isprime(s) and nextprime(s) + prevprime(s) = 2*s then
    count:= count+1; Res:= Res, s;
  fi
od:
Res; # Robert Israel, May 03 2019

Prog

(Magma) [ p: q in PrimesInInterval(3, 110000) | IsPrime(p) and PreviousPrime(p)+NextPrime(p) eq 2*p where p is (PreviousPrime(q)+q+NextPrime(q)-1) div 2];

Crossrefs

Cf. A006562 (balanced primes), A127313, A129190, A129242.

Sequence in context: A195894 A263555 A156835 * A078960 A185515 A185704

Adjacent sequences: A129188 A129189 A129190 * A129192 A129193 A129194

Keyword

nonn

Author

Klaus Brockhaus, Apr 05 2007

Status

approved