

A036057


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


13



25, 121, 125, 126, 127, 128, 153, 216, 289, 343, 347, 625, 688, 736, 1022, 1024, 1206, 1255, 1260, 1285, 1296, 1395, 1435, 1503, 1530, 1792, 1827, 2048, 2187, 2349, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509, 2592, 2737, 2916, 3125, 3159
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OFFSET

1,1


COMMENTS

Mitchell's and Wilson's lists both lack two terms, 16387 = (16/8)^(7)+3 and 41665 = 641*65.  Giovanni Resta, Dec 14 2013
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


LINKS

M. F. Hasler, Table of n, a(n) for n = 1..844 (data from E. Friedman's page as collected by K. Mitchell, completed by the two missing terms found by G. Resta).
M. Brand, Friedman numbers have density 1, Discrete Applied Mathematics, Volume 161, Issues 1617, November 2013, Pages 23892395.
Ed Copeland and Brady Haran, Friedman numbers, Numberphile video, 2014
Erich Friedman, Friedman Numbers
Giovanni Resta, Friedman numbers Friedman numbers and expressions up to 10^6
Robert G. Wilson v, Table of n, a(n) with factorizations for n=1..844
Index entries for Four 4's problem


FORMULA

a(n) ~ n, see Brand.  Charles R Greathouse IV, Jun 04 2013


EXAMPLE

E.g., 153=51*3, 736=3^6+7. Not 26 = 2 6 (concatenated), that's trivial.


CROSSREFS

Cf. A080035, A156954, A046469.
Sequence in context: A078815 A270368 A206472 * A083509 A339130 A256519
Adjacent sequences: A036054 A036055 A036056 * A036058 A036059 A036060


KEYWORD

base,nonn


AUTHOR

Erich Friedman


EXTENSIONS

Edited by Michel Marcus and M. F. Hasler, Jan 04 2015


STATUS

approved



