A281152 Least number k such that Sum_{j=k..k+n-1}{j} = Sum_{j=k+n..t}{j}, for some t >= k+n.

1, 4, 9, 4, 2, 12, 49, 11, 3, 40, 26, 60, 1, 11, 225, 112, 5, 144, 43, 12, 6, 220, 21, 18, 7, 32, 60, 364, 8, 420, 961, 4, 9, 25, 77, 612, 10, 16, 243, 760, 2, 840, 94, 4, 12, 1012, 165, 81, 13, 52, 111, 1300, 14, 24, 340, 67, 15, 1624, 9, 1740, 16, 35, 3969, 46

Offset

2,2

Comments

With n = 5 consecutive numbers we can start from k = 4 but also from k = 16. The sequence considers only the least number: a(5) = 4.

Links

Table of n, a(n) for n=2..65.

Paolo P. Lava, First 500 terms with values for n, k and t

Example

a(2)= 1 because 1+2=3 and 1 is the least number to have this property;
a(3)= 4 because 4+5+6=7+8 and 4 is the least number to have this property;
a(4)= 9 because 9+10+11+12=13+14+15 and 9 is the least number to have this property;
a(5)= 4 because 4+5+6+7+8=9+10+11 and 4 is the least number to have this property.

Maple

P:=proc(q, h) local a, b, c, j, k, n;  for n from 2 to q do for k from 1 to q do a:=add(j^h, j=k..k+n-1); b:=0;
c:=k+n-1; while b<a do c:=c+1; b:=b+c^h; od; if a=b then print(k); break; fi; od; od; end: P(10^6, 1);

Crossrefs

Cf. A281153.

Sequence in context: A189510 A341953 A341767 * A238849 A360697 A197582

Adjacent sequences: A281149 A281150 A281151 * A281153 A281154 A281155

Keyword

nonn,easy

Author

Paolo P. Lava, Jan 16 2017

Status

approved