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

127, 343, 736, 1285, 2187, 2502, 2592, 2737, 3125, 3685, 3864, 3972, 4096, 6455, 11264, 11664, 12850, 13825, 14641, 15552, 15585, 15612, 15613, 15617, 15618, 15621, 15622, 15623, 15624, 15626, 15632, 15633, 15642, 15645, 15655, 15656

Offset: 1

Author

David Rattner (david_rattner(AT)prusec.com), Mar 14 2003

Keywords

• nonn
• base
• nice

Comments

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

Examples

			127 = -1 + 2^7, 343 = (3 + 4) ^ 3, 736 = 7 + 3^6, etc.
The 4th "orderly" Friedman number is 1285 = (1 + 2^8) * 5.
		

References

• Credit goes to Mike Reid (Brown University) and Eric Friedman (Stetson University).
• Colin Rose, "Radical Narcissistic numbers", J. Recreational Mathematics, vol. 33, (2004-2005), pp. 250-254. See page 251.

Links

• Michael 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
• Eric Friedman, Friedman Numbers.
• Shyam Sunder Gupta, Digital Invariants and Narcissistic Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 21, 513-526.
• Robert G. Wilson v, Table of n, a(n) for n = 1..108 .

Crossrefs

Cf. A036057.

Extensions

More terms from Alonso del Arte, Aug 25 2004

Edited by M. F. Hasler, Jan 07 2015