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Search: id:A128925
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| A128925 |
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Primes p such that at least one of the two numbers p^2-6, p^2+6 is prime. |
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1
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| 3, 5, 7, 11, 13, 17, 19, 23, 31, 47, 53, 61, 67, 73, 79, 83, 89, 97, 107, 109, 113, 131, 151, 167, 193, 197, 199, 263, 269, 293, 317, 331, 367, 373, 383, 401, 431, 457, 463, 467, 487, 503, 557, 569, 593, 607, 643, 647, 673, 677, 683, 709, 773, 787, 797, 823, 827
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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p = 5 is the only term for which both p^2 - 6 and p^2 + 6 are primes.
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EXAMPLE
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5^2-6 = 19 is prime (just as is 5^2+6 = 31), hence 5 is in the sequence.
79^2+6 = 6241+6 = 6247 is prime, hence 79 is in the sequence.
83^2-6 = 6889-6 = 6883 is prime, hence 83 is in the sequence.
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MAPLE
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a:=proc(n) if isprime(ithprime(n)^2+6)=true or isprime(ithprime(n)^2-6)=true then ithprime(n) else fi end: seq(a(n), n=1..200); (Emeric Deutsch (deutsch(AT)duke.poly.edu), May 05 2007)
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MATHEMATICA
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Select[ Prime@ Range[2, 145], PrimeQ[ #^2 - 6] || PrimeQ[ #^2 + 6] &] (* Robert G. Wilson v *)
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PROGRAM
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(PARI) {forprime(p=2, 830, s=p^2; if(isprime(s-6)||isprime(s+6), print1(p, ", ")))} /* Klaus Brockhaus, May 06 2007 */
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CROSSREFS
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Cf. A001248 (squares of primes).
Sequence in context: A060770 A120334 A000978 this_sequence A158361 A131261 A100276
Adjacent sequences: A128922 A128923 A128924 this_sequence A128926 A128927 A128928
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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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Edited and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Emeric Deutsch (deutsch(AT)duke.poly.edu), May 01 2007
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