A239878 Numbers k with digit_sum(k*k) + 1 = digit_sum((k+1)*(k+1)).

0, 18, 27, 36, 45, 72, 81, 108, 153, 198, 216, 225, 243, 252, 270, 297, 306, 342, 369, 396, 423, 441, 450, 477, 486, 495, 504, 513, 522, 549, 558, 576, 603, 630, 639, 657, 693, 702, 729, 747, 756, 783, 801, 846, 891, 918, 954, 963, 972, 981

Offset: 1

Author

Reiner Moewald, Mar 28 2014

Keywords

• nonn
• base

Comments

All terms are divisible by 9.

The number of terms is unlimited: n = 3*10^z + 6, i.e., digit_sum(n*n) + 1 = 27 + 1 = 28 = digit_sum((n+1)*(n+1)). - Reiner Moewald, Apr 20 2014

Links

• Reiner Moewald, Table of n, a(n) for n = 1..4067

Crossrefs

Cf. A202089, A240752, A240754, A004159, A007953, A000290.

Programs

Haskell

import Data.List (elemIndices)
a239878 n = a239878_list !! (n-1)
a239878_list = elemIndices 1 a240752_list
-- Reinhard Zumkeller, Apr 12 2014

PARI

isok(n) = (sumdigits(n^2) + 1) == sumdigits((n+1)^2); \\ Michel Marcus, Apr 06 2014

Python

def digit_Sum(n):
   integerString = str(n)
   digit_Sum=0
   for digitLetter in integerString:
      digit_Sum = digit_Sum + int(digitLetter)
   return digit_Sum
count = 0;
for i in range(20000):
   if(digit_Sum(i*i) + 1 == digit_Sum((i+1)*(i+1))):
      count = count +1
      print(count,"   ",i)

Formula

A240752(a(n)) = 1. - Reinhard Zumkeller, Apr 12 2014