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

4, 13, 22, 49, 58, 76, 103, 130, 139, 157, 193, 202, 229, 247, 256, 274, 283, 301, 391, 418, 427, 454, 463, 472, 481, 508, 526, 553, 598, 607, 616, 643, 661, 679, 688, 724, 733, 742, 760, 769, 778, 796, 850, 868, 877, 886, 904, 913, 931, 949, 958, 976, 1003

Offset

1,1

Comments

Or numbers n such that A004159(n)=A004159(n+1), or A007953(n^2)=A007953((n+1)^2).

Corresponding digit sums are of the form 7+9k, with k=1, 2, 3,... .

Numbers n are of the form 4+9m, with m=0, 1, 2, 5, 6, 8, 11, ... .

A240752(a(n)) = 0. - Reinhard Zumkeller, Apr 12 2014

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Example

4^2=16 and 5^2=25 have same digit sum ds=7.
13^2=169 and 14^2=196 have ds=16.
76^2=5776 and 77^2=5929 have ds=25.
526^2=276676 and 527^2=277729 have ds=34.

Mathematica

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]]

Prog

(Haskell)
import Data.List (elemIndices)
a202089 n = a202089_list !! (n-1)
a202089_list = elemIndices 0 a240752_list
-- Reinhard Zumkeller, Apr 12 2014
(Python)
def ok(n): return sum(map(int, str(n*n))) == sum(map(int, str((n+1)**2)))
print(list(filter(ok, range(1004)))) # Michael S. Branicky, Apr 13 2021

Crossrefs

Cf. A004159, A007953.

Cf. A239878, A240754.

Sequence in context: A052218 A341005 A183148 * A339804 A256390 A264623

Adjacent sequences: A202086 A202087 A202088 * A202090 A202091 A202092

Keyword

nonn,base

Author

Zak Seidov, Dec 11 2011

Status

approved