A112419 Prime Friedman numbers.

127, 347, 2503, 12101, 12107, 12109, 15629, 15641, 15661, 15667, 15679, 16381, 16447, 16759, 16879, 19739, 21943, 27653, 28547, 28559, 29527, 29531, 32771, 32783, 35933, 36457, 39313, 39343, 43691, 45361, 46619, 46633, 46643, 46649, 46663, 46691, 48751, 48757, 49277, 58921, 59051, 59053, 59263, 59273, 64513, 74353, 74897, 78163, 83357

Offset: 1

Author

Lekraj Beedassy, Jan 23 2007

Keywords

• nonn
• base

Comments

A Friedman number is one which is expressible in a nontrivial manner with the same digits by means of the arithmetic operations +, -, *, "divided by" along with ^ and digit concatenation.

Ron Kaminsky notes that, by Dirichlet's theorem, this sequence is infinite; see Friedman link. - Charles R Greathouse IV, Apr 30 2010

There are only 49 terms below 10^5, and there are less than 40 "orderly" terms (in A080035) below 10^6. - M. F. Hasler, Jan 03 2015

Examples

			Since the following primes have expressions 16381 = (1+1)^(6+8) - 3 ; 16447 = -1+64+4^7 ; 16759 = 7^5 - 6*(9-1), they are in the sequence.
		

Links

• Erich Friedman, Problem of the Month (August 2000).

Crossrefs

Cf. A036057.

Formula

Intersection of A036057 and A000040. - M. F. Hasler, Jan 03 2015

Extensions

Corrected and extended by Ray Chandler, Apr 24 2010