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A168349 Numbers of the form a^b + c^d where a, b, c and d are the first 4 primes. 3
174, 253, 292, 368, 371, 375, 2212, 2219, 16815, 16816, 78133, 78134 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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

LINKS

Table of n, a(n) for n=1..12.

EXAMPLE

(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

MATHEMATICA

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

CROSSREFS

Sequence in context: A025390 A045257 A025381 * A179136 A249432 A077395

Adjacent sequences:  A168346 A168347 A168348 * A168350 A168351 A168352

KEYWORD

fini,full,nonn

AUTHOR

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

STATUS

approved

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Last modified June 24 05:50 EDT 2017. Contains 288697 sequences.