A061912 a(n) is the smallest m for which sqrt(sum of digits of m^2) = n.
0, 1, 2, 3, 13, 67, 264, 1667, 16667, 94863, 1643167, 29983327, 706399164, 31144643167, 1296109172867, 62441868958167, 6927459779738887, 447213595487659543, 77453069648658793167, 14104963594032775808167, 3146266035952345970972687
Offset: 0
Examples
Sum of digits of 13^2 = sum of digits of 169 = 16 is the first occurrence of 4^2, so a(4) = 13.
Links
- Mathematical Reflections, Solution to Problem J307, Issue 5, 2014, p. 1.
Programs
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Maple
f := []: a := 1: for i from 1 to 10 do for j from 1 do if sqrt(convert(convert(j^2,base,10),`+`)) = i then f := [op(f),j]; a := j; break fi; od; od; f;
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Mathematica
t={}; m=0; Do[While[Sqrt[Total[IntegerDigits[m^2]]] != n, m++]; AppendTo[t, m], {n,0,9}]; t (* Jayanta Basu, May 06 2013 *) -
PARI
a(n) = my(k=0); while(sumdigits(k^2) != n^2, k++); k; \\ Michel Marcus, Jan 07 2017
Extensions
a(11) from John W. Layman, Jan 10 2002
a(12) from Ryan Propper, Jul 07 2005
a(13) from Zak Seidov, Jan 27 2011
a(14) from Donovan Johnson, Jul 10 2012
a(15)-a(20) from Zhining Yang, Jun 21 2024
Comments