

A225909


Numbers that are both a sum of two positive cubes and a difference of two consecutive cubes.


3



91, 217, 1027, 4921, 8587, 14911, 31519, 39331, 106597, 117019, 136747, 185257, 195841, 265519, 281827, 616987, 636181, 684019, 712969, 724717, 736561, 955981, 1200169, 1352737, 1405621, 1771777, 2481571, 2756167, 2937331, 4251871, 4996171, 5262901
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Solutions x to the equations x = a^3 + b^3 = (c+1)^3  c^3 in positive integers. The values of c are A226902.
The intersection of A003325 and A003215.
Subsequence of A225908 = numbers that are both a sum and a difference of two positive cubes.
Shiraishi's solution to Gokai Ampon's equation u^3 + v^3 + w^3 = n^3 (see A023042 and A226903) shows that the sequence is infinite.


REFERENCES

Shiraishi Chochu (aka Shiraishi Nagatada), Shamei Sampu (Sacred Mathematics), 1826.


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..5000
David Eugene Smith and Yoshio Mikami, A History of Japanese Mathematics, Open Court, Chicago, 1914; Dover reprint, 2004; pp. 233235.
Wikipedia (French), Shiraishi Nagatada
Wikipedia (German), Shiraishi Nagatada
Index entries for sequences related to sums of cubes


FORMULA

a(n) = (A226902(n)+1)^3  A226902(n)^3.


EXAMPLE

3^3 + 4^3 = 6^3  5^3 = 91, so 91 is a member.


MATHEMATICA

Select[#[[2]]#[[1]]&/@Partition[Range[5000]^3, 2, 1], Count[ IntegerPartitions[ #, {2}], _?(AllTrue[Surd[#, 3], IntegerQ]&)]>0&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 07 2018 *)


CROSSREFS

Cf. A003215, A003325, A023042, A181123, A225908, A226902, A226903.
Sequence in context: A260064 A207077 A293648 * A051973 A290812 A000864
Adjacent sequences: A225906 A225907 A225908 * A225910 A225911 A225912


KEYWORD

nonn


AUTHOR

Jonathan Sondow, Jun 21 2013


STATUS

approved



