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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
3, 76, 115, 194, 311, 318, 2155, 2162, 16798, 16799, 78116, 78117
OFFSET
1,1
COMMENTS
There are 4! = 24 permutations of 4 elements, because of commutativity of |x|=|- x| sequence has 4!/2 = 12 different terms.
Note that two terms of sequence (3 and 311) are prime numbers.
REFERENCES
Ivan Niven und H. S. Zuckermann, Einfuehrung in die Zahlentheorie, B.I. Mannheim 1976
Friedhelm Padberg, Elementare Zahlentheorie, Spektrum Akademischer Verlag, 2. Auflage 1991
EXAMPLE
(1) 3 = 2^7 - 5^3 = prime(2)
(2) 76 = 2 ^ 2 x 19 = 5^3 - 7^2
(3) 115 = 5 x 23 = 3^5 - 2^7
(4) 194 = 2 x 97 = 3^5 - 7^2
(5) 311 = 7^3 - 2^5 = prime(2^6)
(6) 318 = 2 x 3 x 53 = 7^3 - 5^2
(7) 2155 = 5 x 431 = 3^7 - 2^5
(8) 2162 = 2 x 23 x 47 = 3^7 - 5^2
(9) 16798 = 2 x 37 x 227 = 7^5 - 3^2
(10) 16799 = 107 x 157 = 7^5 - 2^3
(11) 78116 = 2 ^ 2 x 59 x 331 = 5^7 - 3^2
(12) 78117 = 3 x 13 x 2003 = 5^7 - 2^3
CROSSREFS
Cf. A168349.
Sequence in context: A308866 A089301 A037110 * A042267 A201428 A141103
KEYWORD
fini,full,nonn
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 24 2009
STATUS
approved