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
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.
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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
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Select[ Intersection[ Flatten[ Table[ i^2*(i+1)/2 + j^2*(j+1)/2, {i,1,300}, {j,1,i} ] ] ], IntegerQ[ Sqrt[ # ] ] & ]
A136360
Square roots of the perfect squares in A133459.
Original entry on oeis.org
6, 9, 12, 17, 22, 24, 25, 26, 60, 86, 99, 120, 188, 200, 202, 210, 214, 238, 243, 268, 336, 348, 415, 476, 481, 504, 524, 539, 565, 602, 693, 704, 720, 726, 732, 846, 899, 961, 965, 990, 1026, 1202, 1218, 1221, 1224, 1320, 1551, 1602, 1687, 1716, 1724, 1734
Offset: 1
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) = sqrt(36) = 6, a(2) = sqrt(81) = 9, a(3) = sqrt(144) = 12, a(4) = sqrt(289) = 17 that are the square roots of the perfect squares in A133459.
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Sqrt[ Select[ Intersection[ Flatten[ Table[ i^2*(i+1)/2 + j^2*(j+1)/2, {i,1,300}, {j,1,i} ] ] ], IntegerQ[ Sqrt[ # ] ] & ] ]
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
A172425
Pentagonal pyramidal numbers which are the sum of two other such numbers: A002411(k) = A002411(i)+A002411(j) with i,j>0.
Original entry on oeis.org
37926, 279046, 2514726, 34797726, 71254566, 348145726, 566225926, 606245926, 828497488, 1206646551, 8750871976, 11481404326, 21078151200, 28120290876, 62963640936, 75128827176, 77009692800, 96868002726, 120282238710, 147061923750, 165998399400, 297022824126, 325443925926, 416397477888
Offset: 1
A172437
Indices of pentagonal pyramidal numbers which are the sum of two other such numbers: k such that A002411(k) = A002411(i)+A002411(j) for some i,j>0.
Original entry on oeis.org
42, 82, 171, 411, 522, 886, 1042, 1066, 1183, 1341, 2596, 2842, 3480, 3831, 5012, 5316, 5360, 5786, 6219, 6650, 6924, 8406, 8666, 9408, 10707, 11735, 12590, 12891, 14422, 14646, 14826, 17351, 17702, 17757, 18882, 23210, 24108, 25127, 28175, 31980, 32400
Offset: 1
a(1)=42 because A002411(42) is the smallest term in that sequence which is the sum of two other (nonzero) terms of A002411.
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for(n=1,99999,for(m=1,n-1, isA002411(p(n)-p(m)) & !print1(n", ") & break)) /* needs isA002411() and p() */
Showing 1-5 of 5 results.
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