A112419 - OEIS

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

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OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..49.

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

FORMULA

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

EXAMPLE

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.

CROSSREFS

Cf. A036057.

Sequence in context: A283622 A080035 A162004 * A142201 A142889 A095312