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

Author

Erich Friedman

Keywords

• base
• nonn

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

Examples

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

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
• Shyam Sunder Gupta, Digital Invariants and Narcissistic Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 21, 513-526.
• 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

Crossrefs

Cf. A080035, A156954, A046469.

Formula

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

Extensions

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