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A129191 Balanced primes p of the form (r+q+s-1)/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 (list; graph; refs; listen; history; text; internal format)
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+1279-1)/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+r-1)/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

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Last modified July 27 05:04 EDT 2021. Contains 346305 sequences. (Running on oeis4.)