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

0,3

Comments

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

Links

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

Formula

a(n^2) = n^2.

Example

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

Prog

(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
(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

Crossrefs

Cf. A006255.

Sequence in context: A143545 A338155 A328045 * A328722 A143521 A278363

Adjacent sequences: A277275 A277276 A277277 * A277279 A277280 A277281

Keyword

nonn

Author

Peter Kagey, Oct 15 2016

Status

approved