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 A208130 Numbers that when expressed in decimal are equal to the sum of the digits sorted into nondecreasing order and raised to the powers 1, 2, 3, ... 2
 1, 2, 3, 4, 5, 6, 7, 8, 9, 89, 135, 2537, 60409, 4901732, 17735872, 45279768, 393470463, 3623008669, 3893095238, 229386834955666, 1892713761283624, 1501212693940707502, 1517944702855898904, 12303679765763687463, 122947811178635339597, 1095354314191826124704, 1106509957063490820877 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Lemma: The sequence is finite with all terms in the sequence having at most 22 digits. Proof: Let n be an m-digit natural number in the sequence for some m. Then 10^(m-1) <= n and n <= 9 + 9^2 + ... + 9^m = 9(9^m-1)/8 < (9^(m+1))/8. Thus 10^(m-1) < (9^(m+1))/8. Taking logarithms of both sides and solving yields m < 22.97. QED. The sequence listed, found by a computer program searching up to 10^22, is therefore complete. - Francis J. McDonnell, Apr 12 2012 LINKS Francis J. McDonnell, Java program EXAMPLE 2537 = 2^1 + 3^2 + 5^3 + 7^4 = 2 + 9 + 125 + 2401. 60409 = 0^1 + 0^2 + 4^3 + 6^4 + 9^5 = 0 + 0 + 64 + 1296 + 59049. PROG (Java) see link. (Python) from itertools import combinations_with_replacement A208130_list = [] for l in range(1, 23):     for n in combinations_with_replacement(range(10), l):         x = sum(b**(a+1) for a, b in enumerate(n))         if x > 0 and tuple(sorted(int(d) for d in str(x))) == n:             A208130_list.append(x) A208130_list = sorted(A208130_list)  # Chai Wah Wu, May 20 2017 CROSSREFS Cf. A032799 (does not sort the digits prior to raising to powers). Sequence in context: A228326 A098766 A032799 * A160343 A250265 A239085 Adjacent sequences:  A208127 A208128 A208129 * A208131 A208132 A208133 KEYWORD nonn,base,fini,full AUTHOR Francis J. McDonnell, Mar 29 2012 EXTENSIONS More terms added by Francis J. McDonnell, Apr 12 2012 Faster program used to obtain more terms included by Francis J. McDonnell, Apr 16 2012 STATUS approved

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Last modified October 17 11:47 EDT 2019. Contains 328108 sequences. (Running on oeis4.)