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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A256415 A143545 A328045 * A328722 A143521 A278363

Adjacent sequences:  A277275 A277276 A277277 * A277279 A277280 A277281

KEYWORD

nonn

AUTHOR

Peter Kagey, Oct 15 2016

STATUS

approved

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Last modified July 5 00:40 EDT 2020. Contains 335457 sequences. (Running on oeis4.)