

A129191


Balanced primes p of the form (r+q+s1)/2, where r, q, s are consecutive primes.


3



593, 1907, 4409, 6323, 15313, 17483, 19577, 25673, 26693, 29269, 34673, 38867, 46889, 54773, 64013, 67169, 68483, 74567, 81749, 85049, 95273, 96431, 110813, 111863, 127643, 132929, 134213, 134639, 135089, 140351, 156241, 157253, 160403
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OFFSET

1,1


COMMENTS

The primes q arising here are in A129190.
q need not be a balanced prime, see however A129242.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

1907 = (1259+1277+12791)/2 is prime and 1259, 1277, 1279 are consecutive primes. 1907 = A006562(24) is a balanced prime, it has distance 6 to the preceding prime 1901 and to the next prime 1913. Hence 1907 is a term.


MAPLE

p:= 2: q:= 3: r:= 5:
Res:= NULL: count:= 0:
while count < 100 do
p:= q; q:= r; r:= nextprime(r);
s:= (p+q+r1)/2;
if isprime(s) and nextprime(s) + prevprime(s) = 2*s then
count:= count+1; Res:= Res, s;
fi
od:
Res; # Robert Israel, May 03 2019


PROG

(MAGMA) [ p: 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, A129190, A129242.
Sequence in context: A195894 A263555 A156835 * A078960 A185515 A185704
Adjacent sequences: A129188 A129189 A129190 * A129192 A129193 A129194


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Apr 05 2007


STATUS

approved



