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Search: id:A106587
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| A106587 |
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Sum of n-th prime squared and n-th perfect square. |
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1
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| 5, 13, 34, 65, 146, 205, 338, 425, 610, 941, 1082, 1513, 1850, 2045, 2434, 3065, 3770, 4045, 4850, 5441, 5770, 6725, 7418, 8497, 10034, 10877, 11338, 12233, 12722, 13669, 17090, 18185, 19858, 20477, 23426, 24097, 26018, 28013, 29410, 31529, 33722
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) is itself prime for a(1) = 5, a(2) = 13, a(10) = 941, a(20) = 5441, a(30) = 13669, a(34) = 20477, a(36) = 24097, ... a(n) is a semiprime for a(3) = 34 = 2 * 17, a(4) = 65 = 5 * 13, a(5) = 146 = 2 * 73, a(6) = 205 = 5 * 41, a(11) = 1082 = 2 * 541, a(12) = 1513 = 17 * 89, a(14) = 2045 = 5 * 409, a(15) = 2434 = 2 * 1217, a(16) = 3065 = 5 * 613, a(18) = 4045 = 5 * 809, a(23) = 7418 = 2 * 3709, a(24) = 8497 = 29 * 293, a(26) = 10877 = 73 * 149, a(27) = 11338 = 2 * 5669, a(28) = 12233 = 13 * 941, a(29) = 12722 = 2 * 6361, a(32) = 18185 = 5 * 3637, a(33) = 19858 = 2 * 9929, a(37) = 26018 = 2 * 13009, a(38) = 28013 = 109 * 257, a(40) = 31529 = 41 * 769, ... - Jonathan Vos Post (jvospost3(AT)gmail.com), May 14 2005
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EXAMPLE
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a(5)=146 because 121 (fifth prime^2) + 25 (fifth square) = 146.
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MATHEMATICA
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Table[Prime[n]^2 + n^2, {n, 50}]
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CROSSREFS
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Cf. A014688, A076368, A075526, A001248, A000290.
Sequence in context: A147086 A032406 A146917 this_sequence A034509 A034521 A092647
Adjacent sequences: A106584 A106585 A106586 this_sequence A106588 A106589 A106590
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KEYWORD
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easy,nonn
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AUTHOR
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Alexandre Wajnberg (alexandre.wajnberg(AT)ulb.ac.be), May 10 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), May 13 2005
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