A129190 Primes q such that p = (r+q+s-1)/2 is a balanced prime, where r, q, s are consecutive primes.

397, 1277, 2939, 4217, 10211, 11657, 13049, 17117, 17791, 19507, 23117, 25913, 31259, 36523, 42677, 44777, 45659, 49711, 54499, 56701, 63521, 64283, 73877, 74573, 85093, 88609, 89477, 89759, 90059, 93563, 104161, 104831, 106937, 108179

Offset

1,1

Comments

The primes p arising here are in A129191.

q need not be a balanced prime, see however A129241.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

389, 397, 401 are consecutive primes. 593 = (389+397+401-1)/2 = A006562(10) is a balanced prime, it is the average of the preceding prime 587 and the next prime 599. Hence 397 is a term.

Mathematica

bpQ[{r_, q_, s_}]:=Module[{p=(r+q+s-1)/2}, PrimeQ[p]&&Mean[{NextPrime[p], NextPrime[p, -1]}]==p]; Select[Partition[Prime[Range[ 11000]], 3, 1], bpQ][[;; , 2]] (* Harvey P. Dale, Oct 10 2024 *)

Prog

(Magma) [ q: 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, A129191, A129241.

Sequence in context: A142372 A341187 A038660 * A256081 A338476 A152309

Adjacent sequences: A129187 A129188 A129189 * A129191 A129192 A129193

Keyword

nonn

Author

Klaus Brockhaus, Apr 05 2007

Status

approved