A168349 Numbers of the form a^b + c^d where a, b, c and d are the first 4 primes.

174, 253, 292, 368, 371, 375, 2212, 2219, 16815, 16816, 78133, 78134

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 23 2009, Nov 24 2009

Keywords

• fini
• full
• nonn

Comments

There are 4! = 24 permutations of 4 elements, because of commutativity of addition the sequence has 12 different terms.

Note that all terms are composite.

Examples

			(1) 174 = 2 x 3 x 29 = 5^3 + 7^2
(2) 253 = 11 x 23 = 2^7 + 5^3
(3) 292 = 2 ^ 2 x 73 = 3^5 + 7^2
(4) 368 = 2^4 x 23 = 5^2 + 7^3
(5) 371 = 7 x 53 = 2^7 + 3^5
(6) 375 = 3 x 5 ^ 3 = 2^5 + 7^3
(7) 2212 = 2 ^ 2 x 7 x 79 = 3^7 + 5^2
(8) 2219 = 7 x 317 = 2^5 + 3^7
(9) 16815 = 3 x 5 x 19 x 59 = 2^3 + 7^5
(10) 16816 = 2 ^ 4 x 1051 = 3^2 + 7^5
(11) 78133 = 11 x 7103 = 2^3 + 5^7
(12) 78134 = 2 x 7 x 5581 = 3^2 + 5^7
		

References

• Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
• Friedhelm Padberg, Elementare Zahlentheorie, Spektrum Akademischer Verlag, 2. Auflage 1991

Programs

Mathematica

Union[#[[1]]^#[[2]]+#[[3]]^#[[4]]&/@Permutations[Prime[Range[4]]]] (* Harvey P. Dale, Oct 25 2015 *)