A277278 a(n) = smallest m for which there is a sequence n = b_1 < b_2 < ... < b_t = m such that b_1 + b_2 +...+ b_t is a perfect square.

0, 1, 4, 6, 4, 10, 10, 9, 14, 9, 14, 13, 13, 18, 18, 18, 16, 19, 22, 23, 23, 27, 27, 26, 25, 25, 28, 33, 32, 35, 34, 33, 35, 38, 38, 40, 36, 42, 42, 42, 41, 48, 48, 47, 51, 50, 50, 49, 52, 49, 57, 57, 59, 59, 58, 58, 63, 63, 63, 62, 61, 66, 66, 67, 64, 73, 73

Offset: 0

Author

Peter Kagey, Oct 15 2016

Keywords

• nonn

Comments

Sum analog of R. L. Graham's sequence (A006255).

Examples

			a(0) = 0  via 0                  = 0^2
a(1) = 1  via 1                  = 1^2
a(2) = 4  via 2 + 3 + 4          = 3^2
a(3) = 6  via 3 + 6              = 3^2
a(4) = 4  via 4                  = 2^2
a(5) = 10 via 5 + 6 + 7 + 8 + 10 = 6^2
a(6) = 10 via 6 + 10             = 4^2
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..3000

Crossrefs

Cf. A006255.

Programs

Haskell

import Data.List (find)
import Data.Maybe (fromJust)
isSquare m = m == (integerRoot * integerRoot) where
integerRoot = floor (sqrt (fromIntegral m)::Double)
a277278 n
| isSquare n = n
| otherwise = last $ fromJust $ find (isSquare . sum) s where
s = map ((n:) . map (n+)) a048793_tabf
-- Peter Kagey, Oct 19 2016

PARI

a(n)=if (issquare(n), return (n)); ok = 0; d = 1; while (!ok, for (j=1, 2^d-1, b = Vecrev(binary(j)); if (issquare(n+sum(k=1,#b, b[k]*(n+k))), ok = 1; break);); if (! ok, d++);); n+d; \\ Michel Marcus, Oct 16 2016

Formula

a(n^2) = n^2.