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A335205
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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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1
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 48, 407, 5920, 5921, 2918379, 18125436, 210897052, 11647261846, 18107015789, 27434621679, 31332052290, 4986706842391, 485927682264092, 1287253463537089, 1217506990394433558, 11008589751726485523, 107765279704274410345, 109462377410000145640, 109462377410000145641, 118620909850977982494, 319591187568367788829
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OFFSET
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1,3
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COMMENTS
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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.
The last term is smaller than 1.2*10^50. - Jinyuan Wang, May 28 2020
Note that a(14) = a(13) + 1, a(29) = a(28) + 1 - Chai Wah Wu, Jun 03 2020
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LINKS
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EXAMPLE
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5921 is a term because |5^4 - 9^4 + 2^4 - 1^4| = 5921.
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MATHEMATICA
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s[n_] := Block[{d = IntegerDigits@ n}, Abs@ Total[d^Length[d] (-1)^Range@ Length@ d]]; Select[ Range[0, 3*10^6], s[#] == # &]
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PROG
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(PARI) is(k)= my(v=digits(k)); abs(sum(i=1, #v, (-1)^i*v[i]^#v))==k; \\ Jinyuan Wang, May 28 2020
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CROSSREFS
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KEYWORD
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nonn,base,fini,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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