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A138591
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Sums of two or more consecutive integers.
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15
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1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77
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OFFSET
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1,2
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COMMENTS
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Closely related to but different from A057716. - N. J. A. Sloane, May 16 2008
These are called polite numbers [From Howard Berman (howard_berman(AT)hotmail.com), Oct 29 2008] by those who require nonnegative integers in the definition as opposed to positive integers. With the latter requirement, 1 = 0 + 1 does not count as a polite number. [This difference of definition pointed out by Ant King (Nov 19 2010)] There is no disagreement that 1 belongs in this sequence, but there is disagreement as to whether it counts as a polite number.
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REFERENCES
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Melfried Olson, "Sequentially so", Mathematics Magazine 52:5, pp. 297-298.
Wai Yan Pong, "Sums of consecutive integers", The College Mathematics Journal, 38 (2007), 119-123 [From Parthasarathy Nambi, May 20 2009]
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LINKS
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Table of n, a(n) for n=1..71.
Erzsébet Orosz, On odd-summing numbers, Acia Academiae Paedagogicae Agriensis, Seciio Maihemaiicae 31 (2004), pp. 125-129.
Ron Knott, An Introduction to Runsums
NRICH, Polite numbers
PlanetMath, Polite number
Wikipedia, Polite number
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FORMULA
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a(n) = n + A000523(n + A000523(n)) [From Charles R Greathouse IV, Aug 12 2010]
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EXAMPLE
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0+1=1, 1+2=3, 2+3=5, 1+2+3=6, 3+4=7, 4+5=9, 1+2+3+4=10, ...
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MATHEMATICA
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Array[r, 9]; k=0; For[i=0, i<=33, a=i; For[j=i+1, j<=34, a=a+j; k++; r[k]=a; j++ ]; i++ ]; q=Union[Array[r, k]]; StringTake[ToString[q], 99]
1+#+Floor[Log[2, #+1+Log[2, #+1]]] &/@Range[0, 70] ( Ant King, Nov 18 2010).
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CROSSREFS
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Cf. A057716.
Sequence in context: A114309 A079581 A057716 * A136492 A062506 A213199
Adjacent sequences: A138588 A138589 A138590 * A138592 A138593 A138594
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KEYWORD
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nonn,easy
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AUTHOR
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Vladimir Joseph Stephan Orlovsky, May 13 2008
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EXTENSIONS
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More terms from Carl R. White, Jul 22 2009
Comment regarding polite numbers edited by Ant King, Nov 19 2010
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STATUS
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approved
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