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

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

Offset: 1

Author

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

Keywords

• fini
• full
• nonn

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.

Examples

			(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
		

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

Crossrefs

Cf. A168349.