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Numbers of m digits which are equal to the absolute value of the sum of the m-th powers of their digits, with alternating signs.
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%I #25 Jun 03 2020 17:31:37

%S 0,1,2,3,4,5,6,7,8,9,48,407,5920,5921,2918379,18125436,210897052,

%T 11647261846,18107015789,27434621679,31332052290,4986706842391,

%U 485927682264092,1287253463537089,1217506990394433558,11008589751726485523,107765279704274410345,109462377410000145640,109462377410000145641,118620909850977982494,319591187568367788829

%N Numbers of m digits which are equal to the absolute value of the sum of the m-th powers of their digits, with alternating signs.

%C Numbers n equal to |Sum_{j=1..k} (-1)^j*d_j^k| where d_1 d_2 ... d_k is the decimal expansion of n. A variant of narcissistic numbers (A005188), they are finite as well.

%C The last term is smaller than 1.2*10^50. - _Jinyuan Wang_, May 28 2020

%C Note that a(14) = a(13) + 1, a(29) = a(28) + 1 - _Chai Wah Wu_, Jun 03 2020

%e 5921 is a term because |5^4 - 9^4 + 2^4 - 1^4| = 5921.

%t s[n_] := Block[{d = IntegerDigits@ n}, Abs@ Total[d^Length[d] (-1)^Range@ Length@ d]]; Select[ Range[0, 3*10^6], s[#] == # &]

%o (PARI) is(k)= my(v=digits(k)); abs(sum(i=1, #v, (-1)^i*v[i]^#v))==k; \\ _Jinyuan Wang_, May 28 2020

%Y Cf. A005188, A335151.

%K nonn,base,fini,more

%O 1,3

%A _Giovanni Resta_, May 26 2020

%E a(24)-a(25) from _Chai Wah Wu_, May 31 2020

%E a(26) from _Chai Wah Wu_, Jun 01 2020

%E a(27)-a(31) from _Chai Wah Wu_, Jun 03 2020