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A112419 Prime Friedman numbers. 2

%I #13 Aug 13 2020 14:02:28

%S 127,347,2503,12101,12107,12109,15629,15641,15661,15667,15679,16381,

%T 16447,16759,16879,19739,21943,27653,28547,28559,29527,29531,32771,

%U 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

%N Prime Friedman numbers.

%C 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.

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

%C 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

%H Erich Friedman, <a href="https://erich-friedman.github.io/mathmagic/0800.html">Problem of the Month (August 2000)</a>.

%F Intersection of A036057 and A000040. - _M. F. Hasler_, Jan 03 2015

%e 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.

%Y Cf. A036057.

%K nonn,base

%O 1,1

%A _Lekraj Beedassy_, Jan 23 2007

%E Corrected and extended by _Ray Chandler_, Apr 24 2010

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