A138591 -id:A138591 - cp's OEIS frontend

A270306 Smallest number which is representable as a sum of n but no fewer consecutive nonnegative integers, or 0 for n > 1 if no such number exists.

0, 1, 6, 10, 20, 0, 28, 44, 0, 0, 88, 0, 104, 0, 0, 136, 272, 0, 304, 0, 0, 0, 368, 0, 0, 0, 0, 0, 464, 0, 496, 592, 0, 0, 0, 0, 1184, 0, 0, 0, 1312, 0, 1376, 0, 0, 0, 1504, 0, 0, 0, 0, 0, 1696, 0, 0, 0, 0, 0, 1888, 0, 1952, 0, 0, 2144, 0, 0, 4288, 0, 0, 0, 4544

Offset: 1

Martin Renner, Mar 14 2016

nonn

			a(2) = 1 = 0 + 1 (two but no fewer terms)
a(3) = 6 = 1 + 2 + 3 (three but no fewer terms)
a(4) = 10 = 1 + 2 + 3 + 4 (four but no fewer terms)
a(5) = 20 = 2 + 3 + 4 + 5 + 6 (five but no fewer terms)
a(6) = 0, since no number needs six but no fewer terms
a(7) = 28 = 1 + 2 + 3 + 4 + 5 + 6 + 7 (seven but no fewer terms)

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A138591, A163172, A270296 to A270303.

a(A111774(n)) = 0.

a(A174090(n)) = A163172(n).

A158758 Politest numbers.

Original entry on oeis.org

4, 8, 9, 11, 13, 14, 15, 16, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 89, 90

Offset: 1

Vladimir Joseph Stephan Orlovsky, Mar 25 2009

nonn

Politest numbers can be written as the sum of two or more consecutive polite numbers. 1,3,5,6,7,9,10,11,12,13,14,15,17,18,...Polite numbers. 4=1+3, 8=3+5, 9=1+3+5, 11=5+6, 13=6+7, 14=3+5+6, 15=1+3+5+6,...Politest numbers.

Cf. A138591, A065867, A158754

lst={};Do[p=m;If[Mod[2^p,p]!=0||p==1,Do[If[Mod[2^n,n]!=0,p+=n;AppendTo[lst,p]],{n,m+1,5!}]],{m,1,5!}];Take[Union[lst],5! ]

A275535 a(n) = the smallest positive multiple of n that is the sum of more than 1 consecutive positive integers.

Original entry on oeis.org

3, 6, 3, 12, 5, 6, 7, 24, 9, 10, 11, 12, 13, 14, 15, 48, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 96, 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, 192, 65, 66, 67

Offset: 1

Zak Seidov, Aug 01 2016

Surprisingly, first 14 terms coincide with A160899(1)..A160899(14).

			n=1, 3=1+2; n=2, 6 = 1 + 2 + 3; n=3, 3 = 1 + 2; n=4, 12 = 3 + 4 + 5;
n=5, 5=2+3; n=6, 6=1+2+3; n=7, 7=3+4; n=8, 24=7+ 8+ 9;
n=9, 9=4+5; n=10, 10=1+2+3+4; n=11, 11=5+6; n=12, 12=3+4+5;
n=13, 13=6+7; n=14, 14=2+3+4+5; n=15, 15=7+8.

Cf. A138591, A160899.

a:= n-> `if`(2^ilog2(n)=n, 3*n, n):
seq(a(n), n=1..70);  # Alois P. Heinz, Aug 01 2016

a(n)=if(n>>valuation(n,2)==1, 3*n, n) \\ Charles R Greathouse IV, Aug 01 2016

a(n) = 3*n if n is a power of 2, a(n) = n else. - Alois P. Heinz, Aug 01 2016

More terms from Alois P. Heinz, Aug 01 2016

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A270306 Smallest number which is representable as a sum of n but no fewer consecutive nonnegative integers, or 0 for n > 1 if no such number exists.

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A158758 Politest numbers.

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A275535 a(n) = the smallest positive multiple of n that is the sum of more than 1 consecutive positive integers.

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