A147530
Numbers x such that there exists n in N : (x+1)^3 - x^3 = 103*n^2.
Original entry on oeis.org
51721, 6641322533431006, 852782015075257741682069713, 109501859241899449111168441436054160358, 14060635620199598267351285586436862449157290510201, 1805462258017787769335954916623470050495526664967434749114126
Offset: 1
a(1)=51721 because the first relation is : 51722^3 - 51721^3 = 103*8827^2.
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a:=[51721, 6641322533431006];; for n in [3..20] do a[n]:=128405450990*a[n-1] -a[n-2] +62402725494; od; a; # G. C. Greubel, Jan 12 2020
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I:=[51721, 6641322533431006]; [n le 2 select I[n] else 128405450990*Self(n-1) - Self(n-2) + 62402725494: n in [1..20]]; // G. C. Greubel, Jan 12 2020
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seq(coeff(series(x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x + x^2)), x, n+1), x, n), n = 1..20); # G. C. Greubel, Jan 12 2020
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LinearRecurrence[{128405450991,-128405450991,1}, {51721, 6641322533431006, 852782015075257741682069713}, 20] (* G. C. Greubel, Jan 12 2020 *)
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Vec(x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x+x^2)) + O(x^10)) \\ Colin Barker, Oct 21 2014, corrected Jul 13 2016
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isok(x) = issquare(((x+1)^3-x^3)/103) \\ Colin Barker, Jul 13 2016
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def A147530_list(prec):
P. = PowerSeriesRing(ZZ, prec)
return P( x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x + x^2)) ).list()
a=A147530_list(20); a[1:] # G. C. Greubel, Jan 12 2020
A147528
Numbers x such that (x + 103)^3 - x^3 is a square.
Original entry on oeis.org
5327263, 684056220943393618, 87836547552751547393253180439, 11278691501915643258450349467913578516874, 1448245468880558621537182415402996832263200922550703, 185962612575832140241603356412217415201039246491645779158754978
Offset: 1
a(1) = 5327263 because the first relation is : (5327263 + 103)^3 - 5327263^3 = 93645643^2.
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a:=[5327263, 684056220943393618, 87836547552751547393253180439];; for n in [4..20] do a[n]:=128405450991*a[n-1] - 128405450991*a[n-2] + a[n-3]; od; a; # G. C. Greubel, Jan 10 2020
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I:=[5327263, 684056220943393618, 87836547552751547393253180439]; [n le 3 select I[n] else 128405450991*Self(n-1) - 128405450991*Self(n-2) + Self(n-3): n in [1..20]]; // G. C. Greubel, Jan 10 2020
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seq(coeff(series(103*x*(51721 +64202725495*x -51722*x^2)/((1-x)*(1 -128405450990*x +x^2)), x, n+1), x, n), n = 1..20); # G. C. Greubel, Jan 10 2020
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LinearRecurrence[{128405450991, -128405450991, 1}, {5327263, 684056220943393618, 87836547552751547393253180439}, 20] (* G. C. Greubel, Jan 10 2020 *)
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Vec(103*x*(51721+64202725495*x-51722*x^2)/((1-x)*(1-128405450990*x+x^2)) + O(x^20)) \\ Colin Barker, Oct 21 2014
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def A147528_list(prec):
P. = PowerSeriesRing(ZZ, prec)
return P( 103*x*(51721 + 64202725495*x - 51722*x^2) / ((1-x)*(1 -128405450990*x +x^2)) ).list()
a=A147528_list(20); a[1:] # G. C. Greubel, Jan 10 2020
A147529
Numbers n such that there exists x in N : (x+1)^3 - x^3 = 103*n^2.
Original entry on oeis.org
8827, 1133434915879903, 145539221541371657392445143, 18688029378753350610679552570834161667, 2399644840493193509137754319007833077692312755187, 308127477959355126566155341338642382333110448233345362623463
Offset: 1
a(1)=8827 because the first relation is (51721+1)^3 - 51721^3 = 103*8827^2.
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a:=[8827,1133434915879903];; for n in [3..20] do a[n]:=128405450990*a[n-1]+3*a[n-2]-a[n-3]; od; a; # G. C. Greubel, Jan 12 2020
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I:=[8827,1133434915879903]; [n le 2 select I[n] else 128405450990*Self(n-1) - Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 12 2020
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seq(coeff(series(8827*x*(1-x)/(1-128405450990*x+x^2), x, n+1), x, n), n = 1..20); # G. C. Greubel, Jan 12 2020
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LinearRecurrence[{128405450990,-1}, {8827,1133434915879903}, 20] (* G. C. Greubel, Jan 12 2020 *)
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Vec(8827*x*(1-x)/(1-128405450990*x+x^2) + O(x^20)) \\ Colin Barker, Oct 21 2014
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def A147529_list(prec):
P. = PowerSeriesRing(ZZ, prec)
return P( 8827*x*(1-x)/(1-128405450990*x+x^2) ).list()
a=A147529_list(20); a[1:] # G. C. Greubel, Jan 12 2020
Showing 1-3 of 3 results.