A353907 Numbers k such that k equals {alternating sum of digits of k} raised to the power of {number of digits of k}.
1, 2, 3, 4, 5, 6, 7, 8, 9, 31381059609, 1853020188851841
Offset: 1
Examples
31381059609 = (9-0+6-9+5-0+1-8+3-1+3)^11.
Crossrefs
Programs
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Python
def A(n): counter = 0 S = 0 q = n while q: q, c = q//10, q % 10 S += (-1)** counter * c counter += 1 return S ** counter def fixed_points_of_A(): for i in range(1,100): m = int(10 ** (1 - 1/ i)) +1 for k in range(m, 10): n = k**i e = A(n) if n ==e: print(n, k, i) #prints n, the value of the alternating sum, and of the power to which is raised this number.
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