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A138591 Sums of two or more consecutive integers. 15
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

REFERENCES

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]

LINKS

Table of n, a(n) for n=1..71.

Erzs├ębet 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

FORMULA

a(n) = n + A000523(n + A000523(n)) [From Charles R Greathouse IV, Aug 12 2010]

EXAMPLE

0+1=1, 1+2=3, 2+3=5, 1+2+3=6, 3+4=7, 4+5=9, 1+2+3+4=10, ...

MATHEMATICA

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).

CROSSREFS

Cf. A057716.

Sequence in context: A079581 A229858 A057716 * A136492 A062506 A213199

Adjacent sequences:  A138588 A138589 A138590 * A138592 A138593 A138594

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, May 13 2008

EXTENSIONS

More terms from Carl R. White, Jul 22 2009

Comment regarding polite numbers edited by Ant King, Nov 19 2010

STATUS

approved

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Last modified April 20 06:17 EDT 2014. Contains 240779 sequences.