A259372 Smallest number whose sum of squares of some contiguous sectioning of it (into one or more parts) is n.

0, 1, 11, 111, 2, 12, 112, 1112, 22, 3, 13, 113, 222, 23, 123, 1123, 4, 14, 33, 133, 24, 124, 233, 1233, 224, 5, 15, 115, 1115, 25, 125, 1125, 44, 144, 35, 135, 6, 16, 116, 1116, 26, 45, 145, 335, 226, 36, 136, 1136, 444, 7, 17, 117, 46, 27, 127, 1127, 246

Offset

0,3

Comments

This sequence differs from A055016 beginning with a(100): A055016(100) = 68, whereas a(100) = 10.

a(n) = n for n = 0, 1, 101, 1233, ..

Links

Hans Havermann, Table of n, a(n) for n = 0..10000

E. Angelini, Sum of squares -- and a concatenation, SeqFan list, June 23, 2015.

Example

10 may be sectioned into a single part, the (sum of the) square of which is 100. Because it is the smallest number to have a sum of 100, a(100) = 10.
101 may be sectioned into two parts, 10 and 1, the sum of the squares of which is 101. Because it is the smallest number to have a sum of 101, a(101) = 101.
3355 may be sectioned into 3, 35, and 5, the sum of the squares of which is 1259. Because it is the smallest number to have a sum of 1259, a(1259) = 3355.

Mathematica

a[0]=0; a[n_] := Min[ FromDigits/@ Flatten/@ IntegerDigits@ Flatten[ Permutations/@ Sqrt[ IntegerPartitions[ n, {1, 5}, Range[ Sqrt@ n]^2 ]], 1]]; a/@ Range[0, 99] (* Giovanni Resta, Jun 26 2015 *)

Crossrefs

Cf. A055016.

Sequence in context: A266513 A356329 A055016 * A348871 A004287 A061493

Adjacent sequences: A259369 A259370 A259371 * A259373 A259374 A259375

Keyword

nonn,base

Author

Hans Havermann, Jun 25 2015

Status

approved