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A058369
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Numbers n such that n and n^2 have same digit sum.
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11
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0, 1, 9, 10, 18, 19, 45, 46, 55, 90, 99, 100, 145, 180, 189, 190, 198, 199, 289, 351, 361, 369, 379, 388, 450, 451, 459, 460, 468, 495, 496, 550, 558, 559, 568, 585, 595, 639, 729, 739, 775, 838, 855, 900, 954, 955, 990, 999, 1000, 1098, 1099, 1179, 1188, 1189
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A007953(a(n)) = A004159(a(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 25 2009]
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LINKS
| Zak Seidov, Table of n,a(n) for n=1..312205, a(n)=0..10^8
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EXAMPLE
| Digit sum of 9 = 9 9^2 = 81, 8+1 = 9 digit sum of 145 = 1+4+5 = 10 145^2 = 21025, 2+1+0+2+5 = 10 digit sum of 954 = 9+5+4 = 18 954^2 = 910116, 9+1+0+1+1+6 = 18 - Florian Roeseler (hazz_dollazz(AT)web.de), May 03 2010
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MAPLE
| P:=proc(n) local i, k, w, x; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; x:=0; k:=i^2; while k>0 do x:=x+k-(trunc(k/10)*10); k:=trunc(k/10); od; if x=w then print(i); fi; od; end: P(10000); - Paolo P. Lava (paoloplava(AT)gmail.com), Nov 30 2007
sd := proc (n) options operator, arrow: add(convert(n, base, 10)[j], j = 1 .. nops(convert(n, base, 10))) end proc: a := proc (n) if sd(n) = sd(n^2) then n else end if end proc; seq(a(n), n = 0 .. 1400); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), May 11 2010]
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MATHEMATICA
| Select[Range[0, 1200], Total[IntegerDigits[#]]==Total[IntegerDigits[ #^2]]&] (* From Harvey P. Dale, June 14 2011 *)
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PROG
| (Haskell)
import Data.List (elemIndices)
import Data.Function (on)
a058369 n = a058369_list !! (n-1)
a058369_list =
elemIndices 0 $ zipWith ((-) `on` a007953) [0..] a000290_list
-- Reinhard Zumkeller, Aug 17 2011
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CROSSREFS
| Cf. A007953, A058370, A058852.
A077436. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 25 2009]
Sequence in context: A107433 A090570 A131417 * A110939 A141640 A015898
Adjacent sequences: A058366 A058367 A058368 * A058370 A058371 A058372
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KEYWORD
| base,easy,nice,nonn
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AUTHOR
| G. L. Honaker, Jr. (honak3r(AT)gmail.com), Dec 17 2000
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EXTENSIONS
| Edited by N. J. A. Sloane, May 30 2010
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