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A168385 Numbers of the form |a^b - c^d| where a, b, c and d are the first 4 primes. 3

%I

%S 3,76,115,194,311,318,2155,2162,16798,16799,78116,78117

%N Numbers of the form |a^b - c^d| where a, b, c and d are the first 4 primes.

%C There are 4! = 24 permutations of 4 elements, because of commutativity of |x|=|- x| sequence has 4!/2 = 12 different terms.

%C Note that two terms of sequence (3 and 311) are prime numbers.

%D Ivan Niven und H. S. Zuckermann, Einfuehrung in die Zahlentheorie, B.I. Mannheim 1976

%D Friedhelm Padberg, Elementare Zahlentheorie, Spektrum Akademischer Verlag, 2. Auflage 1991

%e (1) 3 = 2^7 - 5^3 = prime(2)

%e (2) 76 = 2 ^ 2 x 19 = 5^3 - 7^2

%e (3) 115 = 5 x 23 = 3^5 - 2^7

%e (4) 194 = 2 x 97 = 3^5 - 7^2

%e (5) 311 = 7^3 - 2^5 = prime(2^6)

%e (6) 318 = 2 x 3 x 53 = 7^3 - 5^2

%e (7) 2155 = 5 x 431 = 3^7 - 2^5

%e (8) 2162 = 2 x 23 x 47 = 3^7 - 5^2

%e (9) 16798 = 2 x 37 x 227 = 7^5 - 3^2

%e (10) 16799 = 107 x 157 = 7^5 - 2^3

%e (11) 78116 = 2 ^ 2 x 59 x 331 = 5^7 - 3^2

%e (12) 78117 = 3 x 13 x 2003 = 5^7 - 2^3

%Y Cf. A168349.

%K fini,full,nonn

%O 1,1

%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 24 2009

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Last modified May 26 07:29 EDT 2022. Contains 354077 sequences. (Running on oeis4.)