

A259372


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


1



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
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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: A281601 A266513 A055016 * A004287 A061493 A093788
Adjacent sequences: A259369 A259370 A259371 * A259373 A259374 A259375


KEYWORD

nonn,base


AUTHOR

Hans Havermann, Jun 25 2015


STATUS

approved



