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A036057 Friedman numbers: can be written in a nontrivial way using their digits and the operations + - * / ^ and concatenation of digits (but not of results).

%I A036057 #39 Mar 20 2025 10:02:20
%S A036057 25,121,125,126,127,128,153,216,289,343,347,625,688,736,1022,1024,
%T A036057 1206,1255,1260,1285,1296,1395,1435,1503,1530,1792,1827,2048,2187,
%U A036057 2349,2500,2501,2502,2503,2504,2505,2506,2507,2508,2509,2592,2737,2916,3125,3159
%N A036057 Friedman numbers: can be written in a nontrivial way using their digits and the operations + - * / ^ and concatenation of digits (but not of results).
%C A036057 Mitchell's and Wilson's lists both lack two terms, 16387 = (1-6/8)^(-7)+3 and 41665 = 641*65. - _Giovanni Resta_, Dec 14 2013
%C A036057 Primes in this sequence are listed in A112419. See also the subsequence A080035 of "orderly" terms, and its subset A156954. - _M. F. Hasler_, Jan 04 2015
%H A036057 M. F. Hasler, <a href="/A036057/b036057.txt">Table of n, a(n) for n = 1..844</a> (data from E. Friedman's page as collected by K. Mitchell, completed by the two missing terms found by G. Resta).
%H A036057 M. 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 A036057 Ed Copeland and Brady Haran, <a href="https://www.youtube.com/watch?v=I7v2wAXFQpc">Friedman numbers</a>, Numberphile video, 2014
%H A036057 Erich Friedman, <a href="https://erich-friedman.github.io/mathmagic/0800.html">Friedman Numbers</a>
%H A036057 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 A036057 Giovanni Resta, <a href="http://www.numbersaplenty.com/set/Friedman_number/">Friedman numbers</a> Friedman numbers and expressions up to 10^6
%H A036057 Robert G. Wilson v, <a href="/A036057/a036057.txt">Table of n, a(n) with factorizations for n=1..844</a>
%H A036057 <a href="/index/Fo#4x4">Index entries for Four 4's problem</a>
%F A036057 a(n) ~ n, see Brand. - _Charles R Greathouse IV_, Jun 04 2013
%e A036057 E.g., 153=51*3, 736=3^6+7. Not 26 = 2 6 (concatenated), that's trivial.
%Y A036057 Cf. A080035, A156954, A046469.
%K A036057 base,nonn
%O A036057 1,1
%A A036057 _Erich Friedman_
%E A036057 Edited by _Michel Marcus_ and _M. F. Hasler_, Jan 04 2015