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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The conjecture in A266212 implies that this sequence has infinitely many terms. LINKS Zhi-Wei Sun, New conjectures on representations of integers (I), Nanjing Univ. J. Math. Biquarterly 34(2017), no. 2, 97-120. 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^3-1-y^4], n=n+1; Print[n, " ", x]; Goto[aa]], {y, 1, (x^3-1)^(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 Zhi-Wei Sun, Dec 24 2015 EXTENSIONS a(17)-a(35) from Lars Blomberg, Dec 30 2015 STATUS approved

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)