|
|
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.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The primes q arising here are in A129241.
Subsequence of A129191, where q need not be balanced.
|
|
LINKS
|
|
|
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.
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|