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A202089 Numbers n such that n^2 and (n+1)^2 have same digit sum. 4
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 (list; graph; refs; listen; history; text; internal format)
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

Moshe Levin, 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

CROSSREFS

Cf. A004159, A007953.

Cf. A239878, A240754.

Sequence in context: A017209 A052218 A183148 * A256390 A264623 A063631

Adjacent sequences:  A202086 A202087 A202088 * A202090 A202091 A202092

KEYWORD

nonn,base

AUTHOR

Moshe Levin, Dec 11 2011

STATUS

approved

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Last modified March 27 04:42 EDT 2017. Contains 284144 sequences.