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Search: id:A002383
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| A002383 |
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Primes of form n^2 + n + 1.
(Formerly M2641 N1051)
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+0
17
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| 3, 7, 13, 31, 43, 73, 157, 211, 241, 307, 421, 463, 601, 757, 1123, 1483, 1723, 2551, 2971, 3307, 3541, 3907, 4423, 4831, 5113, 5701, 6007, 6163, 6481, 8011, 8191, 9901, 10303, 11131, 12211, 12433, 13807, 14281, 17293, 19183, 20023, 20593, 21757
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also primes p such that 4p-3 is square. - Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Sep 07 2005
Also these primes are sums of 1 and some consecutive even numbers starting at 2; e.g. 31=1+2+4+6+8+10. - Labos E. (labos(AT)ana.sote.hu), Apr 15 2003
Also Primes of form n^2 - n + 1 (Prime central polygonal numbers, A002061). - Zak Seidov (zakseidov(AT)yahoo.com), Jan 26 2006
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REFERENCES
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L. Poletti, Le serie dei numeri primi appartenente alle due forme quadratiche (A) n^2+n+1 e (B) n^2+n-1 ..., Atti della Reale Accademia Nazionale dei Lincei, Memorie della Classe di Scienze Fisiche, Matematiche e Naturali, s. 6. 3 (1929), 193-218.
D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 46.
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FORMULA
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a(n) = A002384(n)^2 + A002384(n) + 1 = (A088503(n-1)^2 + 3)/4 = (A110284(n) + 3)/4. - Chandler
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MATHEMATICA
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s=1; Do[s=s+2*n; If[PrimeQ[s], Print[{s, 2*n}]], {n, 1, 100}]
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CROSSREFS
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Cf. A002384, A088503, A110284.
Adjacent sequences: A002380 A002381 A002382 this_sequence A002384 A002385 A002386
Sequence in context: A093431 A083520 A079018 this_sequence A068679 A006978 A060424
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 07 2005
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