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 A138591 Sums of two or more consecutive nonnegative integers. 30
 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. Of course sums of two or more consecutive nonpositive integers have the same absolute values (noted while inserting "nonnegative" in title). All integers are sums of two or more consecutive integers without such restriction. - Rick L. Shepherd, Jun 03 2014 In K-12 education, these are known as "staircase numbers." The "1" is often omitted. - Gordon Hamilton, Mar 17 2015 Complement of A155559. - Ray Chandler, Mar 23 2016 REFERENCES A. Wah and H. Picciotto, Algebra: Themes, Tools, Concepts, 1994, page 190. LINKS Ray Chandler, Table of n, a(n) for n = 1..10000 Ron Knott, An Introduction to Runsums Mathedpage, Staircases NRICH, Polite numbers Melfried Olson, Sequentially so, Mathematics Magazine 52:5, pp. 297-298. Erzsébet Orosz, On odd-summing numbers, Acia Academiae Paedagogicae Agriensis, Seciio Maihemaiicae 31 (2004), pp. 125-129. PlanetMath, Polite number Wai Yan Pong, Sums of consecutive integers, The College Mathematics Journal, 38 (2007), 119-123. - Parthasarathy Nambi, May 20 2009 Wikipedia, Polite number FORMULA a(n) = n + A000523(n + A000523(n)). - 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 1 + # + Floor[Log[2, # + 1 + Log[2, # + 1]]] &/@Range[0, 70] (* Ant King, Nov 18 2010 *) PROG (PARI) a(n)=n+logint(n+logint(n, 2), 2) \\ Charles R Greathouse IV, Sep 01 2015 (PARI) is(n)=n>>valuation(n, 2)>1 || n==1 \\ Charles R Greathouse IV, Aug 01 2016 CROSSREFS Cf. A057716, A155559. Sequence in context: A229858 A269020 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 December 15 01:20 EST 2018. Contains 318141 sequences. (Running on oeis4.)