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 A058369 Numbers n such that n and n^2 have same digit sum. 20
 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; text; internal format)
 OFFSET 1,3 COMMENTS A007953(a(n)) = A004159(a(n)). - Reinhard Zumkeller, Apr 25 2009 It is interesting that the graph of this sequence appears almost identical as the maximum value of n increases by factors of 10. Compare the graph of the b-file (having numbers up to 10^6) with the plot of the terms up to 10^8. - T. D. Noe, Apr 28 2012 If iterated digit sum (A010888, A056992) is used instead of just digit sum (A007953, A004159), we get A090570 of which this sequence is a subset. - Jeppe Stig Nielsen, Feb 18 2015 Hare, Laishram, & Stoll show that this sequence (indeed, even its subsequence A254066) is infinite. In particular for each k in {846, 847, 855, 856, 864, 865, 873, ...} there are infinitely many terms in this sequence not divisible by 10 that have digit sum k. - Charles R Greathouse IV, Aug 25 2015 There are infinitely many n such that both n and n+1 are in the sequence.  This includes A002283. - Robert Israel, Aug 26 2015 LINKS Zak Seidov, Table of n, a(n) for n = 1..8354 (to a(n) = 10^6) K. G. Hare, S. Laishram, and T. Stoll, The sum of digits of n and n^2, International Journal of Number Theory 7:7 (2011), pp. 1737-1752. T. D. Noe, Plot of terms up to 10^8 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 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, 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); # Emeric Deutsch, May 11 2010 select(t -> convert(convert(t, base, 10), `+`)=convert(convert(t^2, base, 10), `+`), [seq(seq(9*i+j, j=0..1), i=0..1000)]); # Robert Israel, Aug 26 2015 MATHEMATICA Select[Range[0, 1200], Total[IntegerDigits[#]]==Total[IntegerDigits[ #^2]]&] (* Harvey P. Dale, Jun 14 2011 *) 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 (PARI) is(n)=sumdigits(n)==sumdigits(n^2) \\ Charles R Greathouse IV, Aug 25 2015 (MAGMA) [n: n in [0..1200] |(&+Intseq(n)) eq (&+Intseq(n^2))]; // Vincenzo Librandi, Aug 26 2015 CROSSREFS Cf. A002283, A007953, A058370, A058852, A077436, A254066. Cf. A147523 (number of numbers in each decade). Sequence in context: A090570 A131417 A268135 * A110939 A260042 A141640 Adjacent sequences:  A058366 A058367 A058368 * A058370 A058371 A058372 KEYWORD base,easy,nice,nonn AUTHOR G. L. Honaker, Jr., Dec 17 2000 EXTENSIONS Edited by N. J. A. Sloane, May 30 2010 STATUS approved

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Last modified October 23 09:28 EDT 2019. Contains 328345 sequences. (Running on oeis4.)