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Search: id:A136204
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| A136204 |
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Primes p such that 3p-2 and 3p+2 are primes (see A125272) and its decimal representation ends in 7. |
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2
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| 7, 37, 127, 167, 257, 337, 757, 797, 887, 1307, 1597, 1657, 1667, 2347, 2557, 2897, 2927, 3067, 4297, 4327, 4877, 5087, 5147, 5227, 5417, 5857, 6337, 6827, 6917, 6967, 7127, 7187, 7547, 7687, 7867, 7877, 8147, 8447, 8527, 8647, 9857, 10037, 10687
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OFFSET
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1,1
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COMMENT
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Theorem: If in the triple (3n-2,n,3n+2) all numbers are primes, then n=5 or the decimal representation of n ends in 3 or 7. Proof: Similar to A136191. Alternative Mathematica proof: Table[nn = 10k + r; Intersection (AT)(AT) (Divisors[CoefficientList[(3nn - 2) nn(3nn + 2), k]]), {r, 1, 9, 2}]; This gives {{1, 5}, {1}, {1, 5}, {1}, {1, 5}}. Therefore only r=3 and r=7 allow non trivial divisors (excluding nn=5 itself).
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MATHEMATICA
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TPrimeQ = (PrimeQ[ # - 2] && PrimeQ[ #/3] && PrimeQ[ # + 2]) &; Select[Select[Range[100000], TPrimeQ]/3, Mod[ #, 10] == 7 &]
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CROSSREFS
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Cf. A136191, A136192, A125272.
Adjacent sequences: A136201 A136202 A136203 this_sequence A136205 A136206 A136207
Sequence in context: A107938 A106064 A038862 this_sequence A139891 A082113 A143991
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KEYWORD
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nonn,base
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AUTHOR
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Carlos Alves (cjsalves(AT)gmail.com), Dec 21 2007
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