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A129190
Primes q such that p = (r+q+s-1)/2 is a balanced prime, where r, q, s are consecutive primes.
3
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
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
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Apr 05 2007
STATUS
approved