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A274033 Numbers n such that n = a^2 + b^4 and n^2 = c^3 + d^5 for some positive integers a, b, c, d. 0
81250, 1062882, 11529602, 12500000, 170061120, 200000000, 2662400000, 5897400777, 7309688832, 12814453125, 34297420960, 37019531250 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In other words, values of a^2 + b^4 such that (a^2 + b^4)^2 is of the form c^3 + d^5 where a, b, c, d > 0.

81250 is the least number with this property.

Sequence is infinite: If n = a^2 + b^4 and n^2 = c^3 + d^5, then n*k^60 = (a*k^30)^2 + (b*k^15)^4 and (n*k^60)^2 = (c*k^40)^3 + (d*k^24)^5. So if n is in this sequence, then n*k^60 is in this sequence for all nonzero values of k.

LINKS

Table of n, a(n) for n=1..12.

EXAMPLE

81250 is a term because 81250 = 175^2 + 15^4 and 81250^2 = 1875^3 + 25^5.

CROSSREFS

Cf. A100293, A111925.

Sequence in context: A252625 A233994 A237942 * A029752 A043608 A249231

Adjacent sequences:  A274030 A274031 A274032 * A274034 A274035 A274036

KEYWORD

nonn,more

AUTHOR

Altug Alkan, Jun 07 2016

EXTENSIONS

a(2)-a(6) from Giovanni Resta, Jun 07 2016

a(7) from Chai Wah Wu, Jun 14 2016

a(8)-a(12) from Chai Wah Wu, Jul 07 2016

STATUS

approved

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Last modified February 28 09:13 EST 2021. Contains 341695 sequences. (Running on oeis4.)