A281153 Least number k such that Sum_{j=k..k+n-1}{j^2} = Sum_{j=k+n..t}{j^2}, for some t >= k+n.

3, 10, 21, 36, 55, 78, 105, 136, 171, 210, 253, 300, 351, 406, 465, 18, 595, 666, 741, 820, 903, 990, 1081, 1176, 1275, 1378, 1485, 1596, 1711, 1830, 1953, 2080, 2211, 4, 2485, 2628, 2775, 12, 3081, 3240, 3403, 3570, 3741, 3916, 4095, 4278, 4465, 4656, 4851, 60

Offset

2,1

Comments

With n = 17 consecutive numbers we can start from k = 18 but also from k = 528. The sequence considers only the least number: a(17) = 18.

In general t = k + 2*(n-1) but sometimes it differs, e.g., for n = 17, 35, 39, 51, 93, 127, 382, etc.

Links

Table of n, a(n) for n=2..51.

Paolo P. Lava, First 250 terms with values for n, k and t

Example

a(2) = 3 because 3^2 + 4^2 = 5^2 and 3 is the least number to have this property;
a(3) = 10 because 10^2 + 11^2 + 12^2 = 13^2 + 14^2 and 10 is the least number to have this property.
a(4) = 21 because 21^2 + 22^2 + 23^2 + 24^2 = 25^2 + 26^2 + 27^2 and 21 is the least number to have this property.
a(5) = 36 because 36^2 + 37^2 + 38^2 + 39^2 + 40^2 = 41^2 + 42^2 + 43^2 + 44^2 and 36 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, 2);

Crossrefs

Cf. A014105, A059255, A281152.

Sequence in context: A097590 A289183 A194141 * A014105 A354329 A146012

Adjacent sequences: A281150 A281151 A281152 * A281154 A281155 A281156

Keyword

nonn,easy

Author

Paolo P. Lava, Jan 16 2017

Status

approved