

A320249


Numbers not of the form [p^c] + [q^c] + [r^c] + [s^c] + [t^c] where p, q, r, s, and t are prime, c = 41/20 = 2.05, and [...] is the floor function.


1



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 44, 46, 47, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 67, 68, 69, 72, 73, 74, 77, 78, 79, 82, 83, 84, 86, 87, 88, 91, 92, 95, 96
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OFFSET

1,2


COMMENTS

Zhang & Li prove that this sequence is finite. More generally, for any 1 < c < 11216182/5471123 = 2.0500694... except c = 2, there are only finitely many numbers not of the form [p^c] + [q^c] + [r^c] + [s^c] + [t^c] where p, q, r, s, and t are prime.
It seems that a(1058) = 15980 is the last term. If there are any further terms they are larger than 7 * 10^12.  Charles R Greathouse IV, Oct 08 2018


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..1058
Min Zhang and Jinjiang Li, On a Diophantine equation with five prime variables, arXiv:1809.04591 [math.NT] (2018)


EXAMPLE

Missing:
20 = [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05]
25 = [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05] + [3^2.05]
30 = [2^2.05] + [2^2.05] + [2^2.05] + [3^2.05] + [3^2.05]
35 = [2^2.05] + [2^2.05] + [3^2.05] + [3^2.05] + [3^2.05]
40 = [2^2.05] + [3^2.05] + [3^2.05] + [3^2.05] + [3^2.05]
43 = [2^2.05] + [2^2.05] + [2^2.05] + [2^2.05] + [5^2.05]
45 = [3^2.05] + [3^2.05] + [3^2.05] + [3^2.05] + [3^2.05]


CROSSREFS

Sequence in context: A051107 A110303 A180493 * A309066 A084981 A326880
Adjacent sequences: A320246 A320247 A320248 * A320250 A320251 A320252


KEYWORD

nonn,fini


AUTHOR

Charles R Greathouse IV, Oct 08 2018


STATUS

approved



