cp's OEIS Frontend

A202089 Numbers n such that n^2 and (n+1)^2 have same digit sum.

%I A202089 #18 Apr 13 2021 18:43:06
%S A202089 4,13,22,49,58,76,103,130,139,157,193,202,229,247,256,274,283,301,391,
%T A202089 418,427,454,463,472,481,508,526,553,598,607,616,643,661,679,688,724,
%U A202089 733,742,760,769,778,796,850,868,877,886,904,913,931,949,958,976,1003
%N A202089 Numbers n such that n^2 and (n+1)^2 have same digit sum.
%C A202089 Or numbers n such that A004159(n)=A004159(n+1), or A007953(n^2)=A007953((n+1)^2).
%C A202089 Corresponding digit sums are of the form 7+9k, with k=1, 2, 3,... .
%C A202089 Numbers n are of the form 4+9m, with  m=0, 1, 2, 5, 6, 8, 11, ... .
%C A202089 A240752(a(n)) = 0. - _Reinhard Zumkeller_, Apr 12 2014
%H A202089 Zak Seidov, <a href="/A202089/b202089.txt">Table of n, a(n) for n = 1..10000</a>
%e A202089 4^2=16 and 5^2=25 have same digit sum ds=7.
%e A202089 13^2=169 and 14^2=196 have ds=16.
%e A202089 76^2=5776 and 77^2=5929 have ds=25.
%e A202089 526^2=276676 and 527^2=277729 have ds=34.
%t A202089 cnt = 0; nn = 10000; n = 4; Reap[While[cnt < nn, While[Total[IntegerDigits[n^2]] != Total[IntegerDigits[(n + 1)^2]], n = n + 9]; cnt++; Sow[n]; n = n + 9]][[2, 1]]
%o A202089 (Haskell)
%o A202089 import Data.List (elemIndices)
%o A202089 a202089 n = a202089_list !! (n-1)
%o A202089 a202089_list = elemIndices 0 a240752_list
%o A202089 -- _Reinhard Zumkeller_, Apr 12 2014
%o A202089 (Python)
%o A202089 def ok(n): return sum(map(int, str(n*n))) == sum(map(int, str((n+1)**2)))
%o A202089 print(list(filter(ok, range(1004)))) # _Michael S. Branicky_, Apr 13 2021
%Y A202089 Cf. A004159, A007953.
%Y A202089 Cf. A239878, A240754.
%K A202089 nonn,base
%O A202089 1,1
%A A202089 _Zak Seidov_, Dec 11 2011