A177770 Conjectured positive numbers which have more than one representation (m,s) as a difference s^2 - m^5, m >= 1, s > 0.

224, 356, 368, 433, 497, 657, 740, 1057, 1060, 1088, 1124, 1377, 1680, 1828, 2400, 2576, 3332, 3357, 3599, 4100, 4324, 4868, 7076, 8001, 8217, 10993, 11268, 11417, 12289, 13312, 14225, 14852, 15025, 15193, 15593, 15633, 17201, 19140, 20132, 20448, 21124

Offset: 1

Author

Artur Jasinski, May 13 2010

Keywords

• nonn

Comments

Warning: terms may be missing, see the Blomberg link.

Examples

			a(1) = 224 = 15^2-1^5 = 16^2-2^5.
a(2) = 356 = 59^2-5^5 = 182^2-8^5.
a(3) = 368 = 20^2-2^5 = 45531^2-73^5.
a(4) = 433 = 26^2-3^5 = 3447^2-26^5.
a(5) = 497 = 23^2-2^5 = 39^2-4^5.
a(6) = 657 = 30^2-3^5 = 41^2-4^5.
a(7) = 740 = 42^2-4^5 = 12842^2-44^5.
a(8) = 1057 = 332^2-2^5 = 1375^2-18^5.
a(9) = 1060 = 94^2-6^5 = 2822^2-24^5.
a(10) = 1088 = 33^2-1^5 = 184^2-8^5.
a(11) = 1124 = 34^2-2^5 = 318^2-10^5.
a(12) = 1377 = 49^2-4^5 = 1574^2-19^5.
a(13) = 1680 = 41^2-1^5 = 52^2-4^5.
a(14) = 1828 = 98^2-6^5 = 186^2-8^5 = 90298^2-96^5.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..9889. The table contains solutions with differences < 10^9 generated for m <= 10^6. No more solutions are found for m <= 10^9.

Crossrefs

Cf. A152412, A177760, A177761, A177763-A177766.

Extensions

Added constraint s>0 to the definition, inserted 368 - R. J. Mathar, May 23 2010

Name clarified, a(25)-a(41) from Lars Blomberg, Aug 13 2013

Representations for a(3) added in Example by Lars Blomberg, Aug 13 2013