cp's OEIS Frontend

A257860 Numbers n such that a digit of n to the power k plus the sum of the other digits of n equals n, where k is a positive integer.

%I A257860 #19 May 22 2025 10:21:42
%S A257860 1,89,132,264,518,739,2407,6579,8200,8201,8202,8203,8204,8205,8206,
%T A257860 8207,8208,8209,32780,32781,32782,32783,32784,32785,32786,32787,32788,
%U A257860 32789,59060,59061,59062,59063,59064,59065,59066,59067,59068,59069,78145,524300,524301,524302,524303,524304,524305,524306,524307,524308,524309,531459,823567,2097178
%N A257860 Numbers n such that a digit of n to the power k plus the sum of the other digits of n equals n, where k is a positive integer.
%C A257860 There are numbers that come in groups of 10, like 8200, 32780 and 524300. But there are also a few stand-alone numbers. Like 531459 (=5+3+1+4+5+9^6).
%C A257860 It is easy to generate large terms in the sequence, for example, 9^104+409 and 9^1047+4561 are the smallest terms with 100 and 1000 digits, respectively. - _Giovanni Resta_, May 12 2015
%e A257860 89 is in the sequence because 89 = 8+9^2.
%e A257860 2407 is in the sequence because 2407 = 2+4+0+7^4.
%e A257860 8202 is in the sequence because 8202 = 8+ 2^13 +0+2, also 8202 = 8+2+0+2^13.
%o A257860 (Python)
%o A257860 def sod(n):
%o A257860     kk = 0
%o A257860     while n > 0:
%o A257860         kk= kk+(n%10)
%o A257860         n =int(n//10)
%o A257860     return kk
%o A257860 for i in range (1,10**7):
%o A257860     for j in range(1,len(str(i))+1):
%o A257860         k=(i//(10**(j-1)))%10
%o A257860         for m in range (2,30):
%o A257860             if i==sod(i)+k**m-k:
%o A257860                 print (i)
%o A257860 (Haskell)
%o A257860 import Data.List (nub); import Data.List.Ordered (member)
%o A257860 a257860 n = a257860_list !! (n-1)
%o A257860 a257860_list = 1 : filter f [1..] where
%o A257860    f x = any (\d -> member (x - q + d) $ ps d) $ filter (> 1) $ nub ds
%o A257860          where q = sum ds; ds = (map (read . return) . show) x
%o A257860    ps x = iterate (* x) (x ^ 2)
%o A257860 -- _Reinhard Zumkeller_, May 12 2015
%Y A257860 Cf. A061209, A130680, A257766, A257768, A257784,
%Y A257860 Cf. A007953.
%K A257860 nonn,base
%O A257860 1,2
%A A257860 _Pieter Post_, May 11 2015
%E A257860 One more term and some missing data added by _Reinhard Zumkeller_, May 12 2015