A129257 Primes p such that k-1, k+1 are composite, where k = absolute value of q^2 - p*r and p, q, r are consecutive primes.

53, 79, 109, 131, 197, 199, 269, 293, 313, 353, 359, 373, 383, 433, 443, 463, 503, 521, 571, 577, 593, 613, 617, 643, 659, 673, 701, 709, 719, 733, 751, 773, 787, 797, 811, 827, 839, 863, 877, 883, 919, 937, 953, 967, 977, 991, 997, 1013, 1031, 1033, 1039

Offset

1,1

Comments

Primes that are not in A127566.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..3000

Example

79, 83, 89 are consecutive primes, 83^2 - 79*89 = -142. Both 141 = 3*47 and 143 = 11*13 are composite, hence 79 is a term.

Mathematica

Transpose[Select[Partition[Prime[Range[200]], 3, 1], AllTrue[Abs[ #[[2]]^2- #[[1]]*#[[3]]]+{1, -1}, CompositeQ]&]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 04 2015 *)

Prog

(Magma) [ p: p in PrimesInInterval(2, 1060) | not IsPrime(k-1) and not IsPrime(k+1) where k is Abs(q^2 - p*r) where r is NextPrime(q) where q is NextPrime(p) ];

Crossrefs

Cf. A127566.

Sequence in context: A043212 A043992 A032421 * A125875 A059245 A268753

Adjacent sequences: A129254 A129255 A129256 * A129258 A129259 A129260

Keyword

nonn

Author

Klaus Brockhaus, Apr 08 2007

Status

approved