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Search: id:A161533
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| A161533 |
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The smallest of three consecutive primes p1<p2<p3, where p2-p1, p3-p2, and p3-p1 are all perfect squares. |
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+0
2
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| 623071, 779377, 1744891, 2055853, 2906887, 3168721, 3540793, 4177573, 4245643, 4245679, 4309957, 4449127, 4833271, 4858981, 5541187, 5550583, 5710531, 5710567, 5856931, 6013591, 6789637, 6855493, 7024627, 7162339, 7340383, 7614847, 8143501
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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By definition, the two gaps p2-p1, p3-p2 and the double gap p3-p1 form a Pythagorean triple.
Gap pairs p1-p2, p3-p2 occur as 36,64, or 64,36 at least through a(n) <= 10^8.
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EXAMPLE
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623071 is the smallest of the consecutive primes 623071, 623107, and 623171 with gaps 623107-623071=36,
623171-623107=64, and the double gap 623171-623071= 100 each a perfect square.
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CROSSREFS
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Cf. A161002, A138198
Sequence in context: A106780 A156866 A122131 this_sequence A053877 A141815 A048924
Adjacent sequences: A161530 A161531 A161532 this_sequence A161534 A161535 A161536
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KEYWORD
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nonn
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AUTHOR
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Ki Punches (ki1212(AT)pocketmail.com), Jun 13 2009
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EXTENSIONS
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5710567 inserted by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 23 2009
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