A076114 a(n) = start of the smallest string of n consecutive positive integers with a square sum, or 0 if no such number exists.

1, 4, 2, 0, 3, 11, 4, 1, 5, 18, 6, 0, 7, 25, 8, 0, 9, 4, 10, 0, 11, 39, 12, 2, 4, 46, 14, 0, 15, 53, 16, 9, 17, 60, 18, 0, 19, 67, 20, 3, 21, 74, 22, 0, 23, 81, 24, 0, 1, 16, 26, 0, 27, 11, 28, 4, 29, 102, 30, 0, 31, 109, 32, 0, 33, 116, 34, 0, 35, 123, 36, 5, 37, 130, 11, 0, 39

Offset: 1

Author

Amarnath Murthy, Oct 09 2002

Keywords

• nonn
• changed

Comments

Equivalently, smallest k such that n(n+2k-1)/2 is a square, 0 if there is no such square. - Ralf Stephan, Mar 23 2003

a(n)=0 if and only if n has the form 4^e*m with e > 0 and m odd. - Dean Hickerson, Mar 25 2003

a(k) = 1 if k is the index of a square triangular number, i.e., k(k+1)/2 is a square, or if k belongs to A001108. If n is odd then a(n) <= (n+1)/2.

Examples

			a(2) = 4, 4+5 = 9 = 3^2. a(8) = 1, 1+2+3+4+5+6+7+8 = 36 = 6^2.
		

Links

• Clement Martin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001108, A001109, A076115.

Programs

PARI

a(n,limit=oo) = { my(o=n*(n+1)/2, k=0); while(k
				

Extensions

More terms from Ralf Stephan, Mar 23 2003