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Search: id:A127566
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| A127566 |
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Primes p such that at least one of k-1, k+1 is prime, where k = absolute value of q^2 - p*r and p, q, r are consecutive primes. |
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3
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| 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 59, 61, 67, 71, 73, 83, 89, 97, 101, 103, 107, 113, 127, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 271, 277, 281, 283, 307, 311, 317, 331
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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k is always an even number.
Agrees with A049545 for the first 26 terms; first divergence is at 109.
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EXAMPLE
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31, 37, 41 are consecutive primes, 31^2 - 37*41 = -556. 557 is prime, hence 31 is a term.
53, 59, 61 are consecutive primes, 59^2 - 53*61 = 248. Both 247 = 13*19 and 249 = 3*83 are composite, hence 53 is not in the sequence.
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PROGRAM
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(MAGMA) [ p: p in PrimesInInterval(2, 335) | IsPrime(k-1) or IsPrime(k+1) where k is Abs(q^2 - p*r) where r is NextPrime(q) where q is NextPrime(p) ]; /* Klaus Brockhaus, Apr 06 2007 */
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CROSSREFS
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Cf. A049545.
Sequence in context: A080191 A073350 A049545 this_sequence A103146 A049555 A052042
Adjacent sequences: A127563 A127564 A127565 this_sequence A127567 A127568 A127569
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KEYWORD
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nonn
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Apr 02 2007
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 06 2007
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