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Search: id:A111774
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| A111774 |
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Numbers that can be written as a sum of at least three consecutive positive integers. |
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+0
5
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| 6, 9, 10, 12, 14, 15, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In this sequence there are no (odd) primes and there are no powers of 2.
So we have only three kinds of natural numbers: the odd primes, the powers of 2 and the numbers that can be represented as a sum of at least three consecutive integers.
Odd primes can only be written as a sum of two consecutive integers. Powers of 2 do not have a representation as a sum of k consecutive integers (other than the trivial n=n, for k=1).
See also A066542, conjectured complementary (in a way) to this sequence (Jon Awbrey, Aug 15 2005)
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REFERENCES
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Nieuw Archief voor Wiskunde 5/6 nr. 2 Problems/UWC, Problem C, Jun 2005, p. 181-182
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LINKS
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Nieuw Archief voor Wiskunde 5/6 nr. 2 Problems/UWC, Problem C: solution of this Problem
J. Spies, SAGE program for computing A111774
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EXAMPLE
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a(1)=6 because 6 is the first number that can be written as a sum of three consecutive positive integers: 6 = 1+2+3.
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MAPLE
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ispoweroftwo := proc(n) local a, t; t := 1; while (n > t) do t := 2*t end do; if (n = t) then a := true else a := false end if; return a; end proc; f:= proc(n) if (not isprime(n)) and (not ispoweroftwo(n)) then return n end if; end proc; seq(f(i), i = 1..150);
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CROSSREFS
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Cf. A000040, A000079, A066542.
Sequence in context: A103092 A104523 A091886 this_sequence A036347 A129492 A053869
Adjacent sequences: A111771 A111772 A111773 this_sequence A111775 A111776 A111777
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KEYWORD
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easy,nonn
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AUTHOR
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Jaap Spies (j.spies(AT)hccnet.nl), Aug 15 2005
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