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Search: id:A130056
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| A130056 |
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Primes prime(n) such that both of the numbers (prime(n+2)^2-prime(n)^2)/2 - 1 and (prime(n+2)^2-prime(n)^2)/2 + 1 are primes. |
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1
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| 7, 19, 37, 61, 67, 71, 97, 107, 127, 157, 229, 349, 419, 443, 673, 743, 751, 877, 937, 947, 967, 1009, 1039, 1063, 1553, 1609, 1637, 1913, 2311, 2381, 2417, 2437, 2687, 2753, 2969, 3067, 3079, 3137, 3313, 3559, 3803, 3911, 3919, 4111, 4157, 4507, 4621
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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a(1)=7 because (13^2 - 7^2)/2 - 1 = 59 and (13^2 - 7^2)/2 + 1 = 61 (59, 61 are both primes),
a(2)=19 because (29^2 - 19^2)/2 - 1 = 239 and (29^2 - 19^2)/2 + 1 = 241,
a(3)=37 because (43^2 - 37^2)/2 - 1 = 239 and (43^2 - 37^2)/2 + 1 = 241, ...
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MAPLE
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ts_p4:=proc(n) local a, b, i, ans; ans := [ ]: for i from 2 by 1 to n do a := (ithprime(i+2)^(2)-ithprime(i)^(2))/2-1: b := (ithprime(i+2)^(2)-ithprime(i)^(2))/2+1: if (isprime(a)=true and isprime(b)=true) then ans := [ op(ans), ithprime(i) ]: fi od; RETURN(ans) end: ts_p4(2000);
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CROSSREFS
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Cf. A130761.
Sequence in context: A152540 A073859 A038847 this_sequence A136057 A023224 A113743
Adjacent sequences: A130053 A130054 A130055 this_sequence A130057 A130058 A130059
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KEYWORD
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nonn
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AUTHOR
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Jani Melik (jani_melik(AT)hotmail.com), Aug 01 2007
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