

A266215


Positive integers x such that x^3  1 = y^4 + z^2 for some positive integers y and z.


2



3, 13, 27, 147, 203, 5507, 15661, 16957, 21531, 29931, 38051, 47171, 57147, 84027, 85547, 90891, 167051, 273651, 337501, 392881, 421715, 566691, 609971, 698113, 914701, 1229283, 1435213, 1564573, 1786587, 1987571, 2523387, 2579377, 2716443, 3760347, 3778273
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OFFSET

1,1


COMMENTS

The conjecture in A266212 implies that this sequence has infinitely many terms.


LINKS

Table of n, a(n) for n=1..35.
ZhiWei Sun, New conjectures on representations of integers (I), Nanjing Univ. J. Math. Biquarterly 34(2017), no. 2, 97120.


EXAMPLE

a(1) = 3 since 3^3  1 = 1^4 + 5^2.
a(2) = 13 since 13^3  1 = 6^4 + 30^2.
a(6) = 5507 since 5507^3  1 = 29^4 + 408669^2.
a(16) = 90891 since 90891^3  1 = 949^4 + 27387137^2.
a(35) = 3778273 since 3778273^3  1 = 85386^4 + 883654380^2.


MATHEMATICA

SQ[n_]:=SQ[n]=n>0&&IntegerQ[Sqrt[n]]
n=0; Do[Do[If[SQ[x^31y^4], n=n+1; Print[n, " ", x]; Goto[aa]], {y, 1, (x^31)^(1/4)}]; Label[aa]; Continue, {x, 1, 10^5}]


CROSSREFS

Cf. A000290, A000578, A000583, A262827, A266003, A266004, A266152, A266153, A266212.
Sequence in context: A099062 A318368 A196014 * A192535 A002304 A117516
Adjacent sequences: A266212 A266213 A266214 * A266216 A266217 A266218


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Dec 24 2015


EXTENSIONS

a(17)a(35) from Lars Blomberg, Dec 30 2015


STATUS

approved



