A129241 Balanced primes q such that p = (r+q+s-1)/2 is a balanced prime, where r, q, s are consecutive primes.

104161, 169313, 449381, 751753, 857321, 915029, 937789, 976501, 981049, 986581, 1138901, 1159889, 1219469, 1370921, 1488749, 1881949, 1903289, 1980073, 2246129, 2329949, 2356609, 2422093, 2514389, 2602429, 2752921, 2857369

Offset

1,1

Comments

The primes p arising here are in A129242.

Subsequence of A129190, where q need not be balanced.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Formula

a(n) = (2*A129242(n) + 1)/3. - Robert Israel, Mar 08 2026

Example

104149, 104161, 104173 are consecutive primes and 104161 = A006562(446) is a balanced prime (distance 12). (104149+104161+104173-1)/2 = 156241 = A006562(629) is a balanced prime, it has distance 12 to the preceding prime 156229 and to the next prime 156253. Hence 104161 is a term.

Maple

R:= NULL: count:= 0:
q:= 3: s:= 5:
while count < 100 do
  r:= q; q:= s; s:= nextprime(s);
  if r + s = 2*q then
     p:= (3*q-1)/2;
     if isprime(p) and prevprime(p) + nextprime(p) = 2*p then
       count:= count+1; R:= R, q;
     fi
  fi
od:
R; # Robert Israel, Mar 08 2026

Prog

(Magma) [ q: q in PrimesInInterval(3, 2900000) | r+s eq 2*q and IsPrime(p) and PreviousPrime(p)+NextPrime(p) eq 2*p where p is (r+q+s-1) div 2 where r is PreviousPrime(q) where s is NextPrime(q) ];

Crossrefs

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

Sequence in context: A205260 A076761 A236007 * A290535 A253709 A235005

Adjacent sequences: A129238 A129239 A129240 * A129242 A129243 A129244

Keyword

nonn

Author

Klaus Brockhaus, Apr 05 2007

Status

approved