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A080035 "Orderly" Friedman numbers (or "good" or "nice" Friedman numbers): Friedman numbers (A036057) where the construction digits are used in the proper order.

%I A080035 #32 Mar 20 2025 10:30:46
%S A080035 127,343,736,1285,2187,2502,2592,2737,3125,3685,3864,3972,4096,6455,
%T A080035 11264,11664,12850,13825,14641,15552,15585,15612,15613,15617,15618,
%U A080035 15621,15622,15623,15624,15626,15632,15633,15642,15645,15655,15656
%N A080035 "Orderly" Friedman numbers (or "good" or "nice" Friedman numbers): Friedman numbers (A036057) where the construction digits are used in the proper order.
%C A080035 Primes in this sequence are listed in A252483. The subsequence A156954 is a simpler variant where no parentheses, unary operations (negation) nor concatenation is allowed. - _M. F. Hasler_, Jan 07 2015
%D A080035 Credit goes to Mike Reid (Brown University) and Eric Friedman (Stetson University).
%D A080035 Colin Rose, "Radical Narcissistic numbers", J. Recreational Mathematics, vol. 33, (2004-2005), pp. 250-254. See page 251.
%H A080035 Michael Brand, <a href="http://dx.doi.org/10.1016/j.dam.2013.05.027">Friedman numbers have density 1</a>, Discrete Applied Mathematics, Volume 161, Issues 16-17, November 2013, Pages 2389-2395.
%H A080035 Ed Copeland and Brady Haran, <a href="https://www.youtube.com/watch?v=I7v2wAXFQpc">Friedman numbers</a>, Numberphile video, 2014
%H A080035 Eric Friedman, <a href="https://erich-friedman.github.io/mathmagic/0800.html">Friedman Numbers</a>.
%H A080035 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_21">Digital Invariants and Narcissistic Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 21, 513-526.
%H A080035 Robert G. Wilson v, <a href="/A080035/a080035.txt">Table of n, a(n) for n = 1..108 </a>.
%e A080035 127 = -1 + 2^7, 343 = (3 + 4) ^ 3, 736 = 7 + 3^6, etc.
%e A080035 The 4th "orderly" Friedman number is 1285 = (1 + 2^8) * 5.
%Y A080035 Cf. A036057.
%K A080035 nonn,base,nice
%O A080035 1,1
%A A080035 David Rattner (david_rattner(AT)prusec.com), Mar 14 2003
%E A080035 More terms from _Alonso del Arte_, Aug 25 2004
%E A080035 Edited by _M. F. Hasler_, Jan 07 2015