A129242 Balanced primes p of the form (r+q+s-1)/2, where r, q, s are consecutive primes and q is a balanced prime.

156241, 253969, 674071, 1127629, 1285981, 1372543, 1406683, 1464751, 1471573, 1479871, 1708351, 1739833, 1829203, 2056381, 2233123, 2822923, 2854933, 2970109, 3369193, 3494923, 3534913, 3633139, 3771583, 3903643, 4129381

Offset

1,1

Comments

The primes q arising here are in A129241.

Subsequence of A129191, where q need not be balanced.

Links

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

Formula

a(n) = (3*A129241(n)-1)/2. - Robert Israel, Mar 08 2026

Example

253969 = (169307+169313+169319-1)/2 = A006562(937) is a balanced prime, it has distance 18 to the preceding prime 253951 and to the next prime 253987. 169307, 169313, 169319 are consecutive primes and 169313 = A006562(666) is a balanced prime (distance 6), hence 253969 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, p;
     fi
  fi
od:
R; # Robert Israel, Mar 08 2026

Mathematica

Select[Select[(Total[#]-1)/2&/@(Select[Partition[Prime[ Range[ 500000]], 3, 1], Last[#]-#[[2]]==#[[2]]-First[#]&]), PrimeQ], NextPrime[#]-# == #-NextPrime[#, -1]&] (* Harvey P. Dale, May 11 2011 *)

Prog

(Magma) [ p: 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), A129191, A129241.

Sequence in context: A347939 A177811 A341118 * A186605 A297060 A377949

Adjacent sequences: A129239 A129240 A129241 * A129243 A129244 A129245

Keyword

nonn

Author

Klaus Brockhaus, Apr 05 2007

Status

approved