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A049343 Numbers n such that 2n and n^2 have same digit sum. 3
0, 2, 9, 11, 18, 20, 29, 38, 45, 47, 90, 99, 101, 110, 119, 144, 146, 180, 182, 189, 198, 200, 245, 290, 299, 335, 344, 351, 362, 369, 380, 398, 450, 452, 459, 461, 468, 470, 479, 488, 495, 497, 639, 729, 794, 839, 848, 900, 929, 954, 990, 999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

An easy way to prove that this sequence is infinite is to observe that it contains all numbers of the form 10^k+1. - Stefan Steinerberger, Mar 31 2006

For n>0: digital root (A010888) of 2n or n^2 is either 4 or 9. - Reinhard Zumkeller, Oct 01 2007

REFERENCES

Problem 117 in Loren Larson's translation of Paul Vaderlind's book.

LINKS

Reinhard Zumkeller and Harvey P. Dale, Table of n, a(n) for n = 1..1000 (first 101 terms from Zumkeller)

FORMULA

A007953(A005843(a(n))) = A007953(A000290(a(n))). - Reinhard Zumkeller, Oct 01 2007

MATHEMATICA

Select[Range[0, 1000], Sum[DigitCount[2# ][[i]]*i, {i, 1, 9}] == Sum[DigitCount[ #^2][[i]]*i, {i, 1, 9}] &] (* Stefan Steinerberger, Mar 31 2006 *)

Select[Range[0, 1000], Total[IntegerDigits[2#]]==Total[ IntegerDigits[ #^2]]&] (* Harvey P. Dale, Sep 25 2012 *)

PROG

(Haskell)

import Data.List (elemIndices)

import Data.Function (on)

a049343 n = a049343_list !! (n-1)

a049343_list = elemIndices 0

   $ zipWith ((-) `on` a007953) a005843_list a000290_list

-- Reinhard Zumkeller, Apr 03 2011

(MAGMA) [n: n in [0..1000] | &+Intseq(2*n) eq &+Intseq(n^2)]; // Vincenzo Librandi, Nov 17 2015

CROSSREFS

Cf. A058369, A077436 (binary). - Reinhard Zumkeller, Apr 03 2011

Sequence in context: A098934 A237877 A043307 * A131140 A022114 A041099

Adjacent sequences:  A049340 A049341 A049342 * A049344 A049345 A049346

KEYWORD

nonn,base,easy,nice,look

AUTHOR

R. K. Guy

STATUS

approved

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Last modified March 21 01:18 EDT 2019. Contains 321356 sequences. (Running on oeis4.)