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

0,3

Comments

a(15) <= 62441868958167. - Donovan Johnson, Jul 10 2012

a(21) <= 29999999949999914454883190583. a(22) <= 948566760423324122079007168333. - Zhining Yang, Jun 21 2024

Links

Table of n, a(n) for n=0..20.

Mathematical Reflections, Solution to Problem J307, Issue 5, 2014, p. 1.

Example

Sum of digits of 13^2 = sum of digits of 169 = 16 is the first occurrence of 4^2, so a(4) = 13.

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;

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 *)

Prog

(PARI) a(n) = my(k=0); while(sumdigits(k^2) != n^2, k++); k; \\ Michel Marcus, Jan 07 2017

Crossrefs

Cf. A007953, A004159, A061909, A061910, A061911, A067072.

Cf. A067075, A286650.

Sequence in context: A068945 A219698 A293251 * A212433 A013167 A224239

Adjacent sequences: A061909 A061910 A061911 * A061913 A061914 A061915

Keyword

nonn,base,more

Author

Asher Auel, May 17 2001

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

Status

approved