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.
[2^n-n^4: n in [0..30]]; // Vincenzo Librandi, Apr 29 2011
I:=[1,1,-12,-73,-240,-593]; [n le 6 select I[n] else 7*Self(n-1)-20*Self(n-2)+30*Self(n-3)-25*Self(n-4)+11*Self(n-5)-2*Self(n-6): n in [1..35]]; // Vincenzo Librandi, Oct 06 2014
seq(2^n-n^4, n=0..100); # Robert Israel, Oct 06 2014
Table[2^n-n^4,{n,0,100}]
CoefficientList[Series[(1 - 6 x + x^2 + x^3 + 26 x^4 + x^5)/((1 - 2 x) (1 - x)^5), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 06 2014 *)
[10^n-n^10: n in [0..20]]; // Vincenzo Librandi, Jun 30 2011
lst={}; Do[AppendTo[lst,10^n-n^10],{n,0,5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 15 2009 *)
Table[10^n-n^10,{n,0,20}] (* Harvey P. Dale, Apr 22 2018 *)
[12^n-n^12: n in [0..20]]; // Vincenzo Librandi, Jun 30 2011
Table[12^n-n^12,{n,0,30}] (* Harvey P. Dale, Jan 27 2019 *)
[11^n-n^11: n in [0..20]]; // Vincenzo Librandi, Jun 30 2011
Table[11^n - n^11, {n, 0, 20}] (* Harvey P. Dale, Jul 31 2013 *)
a(2) = 8023 because 8023 = 71*113 = 2^13 - 13^2 = 2^A099481(2) - A099481(2)^2.
Select[Table[2^n - n^2, {n, 100}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 21 2012 *)
a(1) = 11 because 2^11 - 11^2 = 1927 = 41*47.
[1-n^2*2^n: n in [0..30]]; // Vincenzo Librandi, Jul 18 2016
f[n_]:=2^n-n^2; Table[Numerator[f[n]],{n,0,-50,-1}]
LinearRecurrence[{7,-18,20,-8},{1,-1,-15,-71},30] (* Harvey P. Dale, May 14 2019 *)
Vec(-(4*x^3-10*x^2+8*x-1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ Colin Barker, Feb 10 2015
a(2) = 2^2 - 2^2 = 0, a(3) = 2^3 - 3 = 5, a(4) = 2^4 - 4^2 = 0, a(5) = 2^5 - 5^2 = 7, a(6)..a(9) are 2^n - n^2, a(10)..a(15) are 2^n - n^3, a(16)..a(22) are 2^n - n^4, and so on.
[2^n - n^Floor(n*Log(n, 2)): n in [2..40]]; // Vincenzo Librandi, Jan 14 2019
Table[2^n - n^Floor[n*Log[n, 2]], {n, 2, 35}] (* T. D. Noe, Aug 27 2012 *)
for n in range(2,100):
a = 2**n
k = 0
while n**(k+1) <= a:
k += 1
print(a - n**k, end=',')
17 = 2^3 + 3^2 = 3^2 + 2^3 is not in the sequence because {2,3} = {3,2} are not distinct.
25 = 3^3 + 2^4 = 3^3 + 4^2 is not in the sequence because 3^3 = 3^3 and 2^4 = 4^2 are commutative.
The smallest term of the sequence is:
a(1) = 432 = 3^2 + 5^2 + 2^6 + 3^4 + 5^3 + 2^7
= 2^3 + 2^5 + 6^2 + 4^3 + 3^5 + 7^2.
The smallest term that has more than one representation is:
a(11) = 1554 = 3^2 + 7^2 + 6^3 + 2^8 + 4^5
= 2^3 + 2^7 + 3^6 + 8^2 + 5^4,
a(11) = 1554 = 3^2 + 5^2 + 2^6 + 10^2 + 2^7 + 3^5 + 2^8 + 3^6
= 2^3 + 2^5 + 6^2 + 2^10 + 7^2 + 5^3 + 8^2 + 6^3.
Smallest terms with k = 5, 6, 7, 8, 9, 10 summands are:
a(9) = 1422 = 5^2 + 7^2 + 9^2 + 3^5 + 4^5
= 2^5 + 2^7 + 2^9 + 5^3 + 5^4,
a(1) = 432 = 3^2 + 5^2 + 2^6 + 3^4 + 5^3 + 2^7
= 2^3 + 2^5 + 6^2 + 4^3 + 3^5 + 7^2,
a(2) = 592 = 3^2 + 5^2 + 7^2 + 4^3 + 2^6 + 5^3 + 2^8
= 2^3 + 2^5 + 2^7 + 3^4 + 6^2 + 3^5 + 8^2,
a(11) = 1554 = 3^2 + 5^2 + 2^6 + 10^2 + 2^7 + 3^5 + 2^8 + 3^6
= 2^3 + 2^5 + 6^2 + 2^10 + 7^2 + 5^3 + 8^2 + 6^3,
a(14) = 1713 = 3^2 + 2^5 + 6^2 + 8^2 + 4^3 + 2^7 + 3^5 + 2^9 + 5^4
= 2^3 + 5^2 + 2^6 + 2^8 + 3^4 + 7^2 + 5^3 + 9^2 + 4^5,
a(28) = 2451 = 3^2 + 5^2 + 6^2 + 8^2 + 3^4 + 2^7 + 6^3 + 3^5 + 5^4 + 2^10
= 2^3 + 2^5 + 2^6 + 2^8 + 4^3 + 7^2 + 3^6 + 5^3 + 4^5 + 10^2.
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