The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A123295 Sum of 14 positive 5th powers. 4
 14, 45, 76, 107, 138, 169, 200, 231, 256, 262, 287, 293, 318, 324, 349, 355, 380, 386, 411, 417, 442, 448, 473, 498, 504, 529, 535, 560, 566, 591, 597, 622, 628, 653, 659, 684, 715, 740, 746, 771, 777, 802, 808, 833, 839, 864, 870, 895, 926, 957, 982, 988 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Up to 417 = 13*(2^5) + 1 this sequence is identical to x+2 for x in A003357 Sum of 12 positive 5th powers. Primes in this sequence (107, 293, 349, 653, ...) are A123300. As proved by J.-R. Chen in 1964, g(5) = 37, so every positive integer can be written as the sum of no more than 37 positive 5th powers. G(5) <= 17, bounding the least integer G(5) such that every positive integer beyond a certain point (i.e., all but a finite number) is the sum of G(5) 5th powers. LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Waring's Problem. FORMULA Sumset {A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584}. EXAMPLE a(1) = 14 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5. a(2) = 45 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5. a(9) = 256 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 3^5. a(11) = 287 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 MATHEMATICA up = 1000; q = Range[up^(1/5)]^5; a ={0}; Do[b = Select[ Union@ Flatten@ Table[e + a, {e, q}], # <= up &]; a=b, {k, 14}]; a (* Giovanni Resta, Jun 12 2016 *) CROSSREFS Cf. A000584, A003336, A003347, A003349, A003350, A003351, A003352, A003353, A003354, A003355, A003356, A003357, A123294-A123297, A008480, A123299, A123300. Sequence in context: A064348 A206215 A328243 * A092350 A090197 A010742 Adjacent sequences:  A123292 A123293 A123294 * A123296 A123297 A123298 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Sep 24 2006 EXTENSIONS 5 missing terms and more terms from Giovanni Resta, Jun 12 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)