

A129242


Balanced primes p of the form (r+q+s1)/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
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OFFSET

1,1


COMMENTS

The primes q arising here are in A129241.
Subsequence of A129191, where q need not be balanced.


LINKS

Table of n, a(n) for n=1..25.


EXAMPLE

253969 = (169307+169313+1693191)/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+s1) div 2 where r is PreviousPrime(q) where s is NextPrime(q) ];


CROSSREFS

Cf. A006562 (balanced primes), A129191, A129241.
Sequence in context: A156118 A171658 A177811 * A186605 A297060 A114658
Adjacent sequences: A129239 A129240 A129241 * A129243 A129244 A129245


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Apr 05 2007


STATUS

approved



