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

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

Offset

1,1

Comments

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

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 16-17, November 2013, Pages 2389-2395.

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 A343075 A339130

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