cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A136361 Square roots of the perfect squares in A136360; or numbers k such that k^4 is in A133459 = the sums of two nonzero pentagonal pyramidal numbers.

Original entry on oeis.org

3, 5, 31, 132, 1068, 9672, 50664, 145060
Offset: 1

Views

Author

Alexander Adamchuk, Dec 25 2007

Keywords

Comments

Corresponding perfect squares in A136360 are a(n)^2 = {9, 25, 961, 17424, ...}. They correspond to the perfect fourth powers in A133459 = Sums of two nonzero pentagonal pyramidal numbers. a(n)^4 are the terms of A133459: {81, 525, 923521, 303595776, ...}. Note that the first three terms are prime.
a(9) > (5*10^20)^(1/4). - Donovan Johnson, Jun 12 2011

Crossrefs

Cf. A136359, A136360, A133459, A002311, A002411, A053721.

Extensions

Name corrected and a(5)-a(6) from Donovan Johnson, Nov 20 2010
a(7)-a(8) from Donovan Johnson, Jun 12 2011

A136359 Perfect squares in A133459; or perfect squares that are the sums of two nonzero pentagonal pyramidal numbers.

Original entry on oeis.org

36, 81, 144, 289, 484, 576, 625, 676, 3600, 7396, 9801, 14400, 35344, 40000, 40804, 44100, 45796, 56644, 59049, 71824, 112896, 121104, 172225, 226576, 231361, 254016, 274576, 290521, 319225, 362404, 480249, 495616, 518400, 527076, 535824
Offset: 1

Views

Author

Alexander Adamchuk, Dec 25 2007

Keywords

Comments

Corresponding numbers m such that m^2 = a(n) are listed in A136360.
Note that some numbers in A136360 are also perfect squares. The corresponding numbers k such that m = k^2 are listed in A136361.
Includes all nonzero members of A099764: this occurs when the two pentagonal pyramidal numbers are both equal to i^2*(i+1)/2 where i+1 is a square. - Robert Israel, Feb 04 2020

Examples

			A133459 begins {2, 7, 12, 19, 24, 36, 41, 46, 58, 76, 80, 81, 93, 115, 127, 132, 144, 150, 166, 197, 201, 202, 214, 236, 252, 271, 289, ...}.
Thus a(1) = 36, a(2) = 81, a(3) = 144, a(4) = 289 that are the perfect squares in A133459.

Links

Crossrefs

Cf. A136360, A136361, A133459, A002311, A002411, A053721, A099764.

Programs

  • Maple
    N:= 200: # for terms up to N^2*(N+1)/2.
PP:= [seq(i^2*(i+1)/2, i=1..N)]:
PP2:= sort(convert(select(`<=`,{seq(seq(PP[i]+PP[j],j=i..N),i=1..N)},PP[-1]),list)):
select(issqr,PP2); # Robert Israel, Feb 04 2020
  • Mathematica
    Select[ Intersection[ Flatten[ Table[ i^2*(i+1)/2 + j^2*(j+1)/2, {i,1,300}, {j,1,i} ] ] ], IntegerQ[ Sqrt[ # ] ] & ]

Formula

a(n) = A136360(n)^2.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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