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

1,1

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

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

Table of n, a(n) for n=1..36.

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 .

Example

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

Crossrefs

Cf. A036057.

Sequence in context: A142165 A031933 A283622 * A162004 A112419 A142201

Adjacent sequences: A080032 A080033 A080034 * A080036 A080037 A080038

Keyword

nonn,base,nice

Author

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

Extensions

More terms from Alonso del Arte, Aug 25 2004

Edited by M. F. Hasler, Jan 07 2015

Status

approved