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Search: id:A128926
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| A128926 |
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Smaller member p of a pair of consecutive primes (p,q) such that either q^2-p^2+1 or q^2-p^2-1 is also prime. |
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+0
1
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| 3, 5, 7, 11, 17, 19, 23, 31, 37, 41, 43, 47, 53, 59, 61, 73, 79, 83, 89, 101, 103, 107, 109, 113, 127, 131, 139, 149, 151, 163, 167, 173, 179, 181, 191, 193, 199, 211, 223, 227, 229, 233, 241, 251, 257, 263, 281, 307, 311, 313, 331, 337, 353, 359, 367, 373, 379
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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3 and 5 are consecutive primes, 5^2-3^2 = 25-9 = 16. 17 is prime, hence 3 is in the sequence.
79 and 83 are consecutive primes, 83^2-79^2 = 6889-6241 = 648. 647 is prime, hence 79 is in the sequence.
89 and 97 are consecutive primes, 97^2-89^2 = 9409-7921 = 1488. 1487 (as well as 1489) is prime, hence 89 is in the sequence.
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MAPLE
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isA128926 := proc(n) local p, q ; p := ithprime(n) ; q := ithprime(n+1) ; isprime((p+q)*(q-p)+1) or isprime((p+q)*(q-p)-1) ; end: for n from 1 to 100 do if isA128926(n) then printf("%d, ", ithprime(n)) ; fi ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 26 2007
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MATHEMATICA
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Prime@ Select[ Range@ 75, PrimeQ[ Prime[ # + 1]^2 - Prime@#^2 - 1] || PrimeQ[ Prime[ # + 1]^2 - Prime@#^2 + 1] &] (* Robert G. Wilson v *)
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PROGRAM
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(MAGMA) [ p: p in PrimesUpTo(380) | IsPrime(q^2-p^2-1) or IsPrime(q^2-p^2+1) where q is NextPrime(p) ]; /* Klaus Brockhaus, May 05 2007 */
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CROSSREFS
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Cf. A069482.
Sequence in context: A116959 A091305 A085498 this_sequence A139559 A048184 A045396
Adjacent sequences: A128923 A128924 A128925 this_sequence A128927 A128928 A128929
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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 25 2007
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EXTENSIONS
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Corrected and extended by Robert G. Wilson v (rgwv(at)rgwv.com), R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 26 2007
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