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A122797
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A P_3-stuttered arithmetic progression with a(n+1) = a(n) if n is a triangular number, a(n+1) = a(n) + 1 otherwise.
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14
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1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 28, 29, 29, 30, 31, 32, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 79, 80, 81, 82, 83, 84, 85, 86, 87
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OFFSET
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1,3
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COMMENTS
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P_3(i) = the i-th triangular number.
As a triangle [1; 1,2; 2,3,4; ...], row sums = A064808: (1, 3, 9, 22, 45, 81, ...). - Gary W. Adamson, Aug 10 2007
a(n) = n - A003056(n-1). - Reinhard Zumkeller, Feb 12 2012
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Grady D. Bullington, The Connell Sum Sequence, J. Integer Seq. 10 (2007), Article 07.2.6. (includes direct formula for a(n))
Douglas E. Iannucci and Donna Mills-Taylor, On Generalizing the Connell Sequence, J. Integer Sequences, Vol. 2, 1999, #99.1.7.
J. W. Meijer and M. Nepveu, Euler's ship on the Pentagonal Sea, Acta Nova, Volume 4, No.1, December 2008. pp. 176-187. [From Johannes W. Meijer, Jun 21 2010]
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FORMULA
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a(n) = A001614(n) - n + 1.
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MATHEMATICA
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nxt[{n_, a_}]:={n+1, If[OddQ[Sqrt[8n+1]], a, a+1]}; NestList[nxt, {1, 1}, 100][[All, 2]] (* Harvey P. Dale, Oct 10 2018 *)
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PROG
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(Haskell)
a122797 n = a122797_list !! (n-1)
a122797_list = 1 : zipWith (+) a122797_list (map ((1 -) . a010054) [1..])
-- Reinhard Zumkeller, Feb 12 2012
(PARI) isTriang(n) = {if (! issquare(8*n+1), return (0)); return (1); }
lista(m) = {aa = 1; for (i=1, m, print1(aa, ", "); if (! isTriang(i), aa = aa + 1); ); } \\ Michel Marcus, Apr 01 2013
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CROSSREFS
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Cf. A001614, A122793, A122794, A122795, A122796, A122798, A122799, A122800.
Cf. A064808.
Sequence in context: A125229 A213855 A272206 * A281957 A286389 A309945
Adjacent sequences: A122794 A122795 A122796 * A122798 A122799 A122800
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KEYWORD
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nonn,easy
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AUTHOR
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Grady Bullington (bullingt(AT)uwosh.edu), Sep 14 2006
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EXTENSIONS
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Definition corrected by Michel Marcus, Apr 01 2013
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STATUS
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approved
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