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.

Showing 1-4 of 4 results.

A147975 a(n) = 4^n-3^n-2^n-1.

Original entry on oeis.org

-2, -2, 2, 28, 158, 748, 3302, 14068, 58718, 241948, 988502, 4015108, 16241678, 65506348, 263636102, 1059360148, 4251855038, 17050597948, 68331794102, 273715121188, 1096023794798, 4387584060748, 17560800790502, 70274592610228
Offset: 1

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Author

Keywords

Crossrefs

Programs

  • Mathematica
    lst={};Do[p=4^n-3^n-2^n-1^n;AppendTo[lst,p],{n,0,5!}];lst
    LinearRecurrence[{10,-35,50,-24},{-2,-2,2,28},40] (* Harvey P. Dale, Nov 08 2016 *)
  • PARI
    a(n)=4^n-3^n-2^n-1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: 2*x*(19*x^3-24*x^2+9*x-1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Oct 29 2012

A147979 a(n) = 8^n-7^n-6^n-5^n-4^n-3^n-2^n-1.

Original entry on oeis.org

-6, -20, -76, -272, -580, 3760, 77324, 896848, 8869820, 81550960, 719926124, 6196609168, 52439953820, 438516694960, 3635082523724, 29935019892688, 245264010263420, 2001462391659760, 16280541150478124, 132087583623451408
Offset: 1

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Author

Keywords

Crossrefs

Programs

  • Mathematica
    lst={};Do[p=8^n-7^n-6^n-5^n-4^n-3^n-2^n-1^n;AppendTo[lst,p],{n,0,5!}];lst
    Table[8^n-Total[Range[7]^n],{n,0,20}] (* or *) LinearRecurrence[{36,-546,4536,-22449,67284,-118124,109584,-40320},{-6,-20,-76,-272,-580,3760,77324,896848},20] (* Harvey P. Dale, Nov 15 2014 *)
  • PARI
    a(n)=8^n-7^n-6^n-5^n-4^n-3^n-2^n-1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: 2*x*(49752*x^7-105056*x^6+87794*x^5-38129*x^4+9380*x^3-1316*x^2+98*x-3)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)). - Colin Barker, Oct 29 2012

A147978 a(n) = 7^n-6^n-5^n-4^n-3^n-2^n-1.

Original entry on oeis.org

-5, -14, -42, -98, 126, 4606, 50478, 446782, 3622206, 28040446, 211134798, 1561328062, 11403051486, 82538901886, 593482158318, 4245770823742, 30254894691966, 214923605948926, 1522969836817038, 10770185918341822
Offset: 1

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Author

Keywords

Crossrefs

Programs

  • Mathematica
    lst={};Do[p=7^n-6^n-5^n-4^n-3^n-2^n-1^n;AppendTo[lst,p],{n,0,5!}];lst

Formula

G.f.: x*(11628*x^6-22736*x^5+17059*x^4-6370*x^3+1260*x^2-126*x+5)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)). - Colin Barker, Oct 29 2012

A240507 Numbers k such that 6^k - 5^k - 4^k - 3^k - 2^k - 1 is prime.

Original entry on oeis.org

4, 6, 12, 16, 34, 48, 68, 384, 1080, 5892, 9816, 34008, 50034, 128256
Offset: 1

Views

Author

Derek Orr, Apr 06 2014

Keywords

Comments

a(11) > 7500.
All terms are even. - Jon Perry, Apr 12 2014

Examples

			6^4 - 5^4 - 4^4 - 3^4 - 2^4 - 1 = 317 is prime. Thus, 4 is a term.
		

Crossrefs

Programs

  • PARI
    for(n=1,7500,if(ispseudoprime(6^n-5^n-4^n-3^n-2^n-1),print(n)))
    
  • Python
    from sympy import isprime
    def afind(limit, k0=1):
        pow6, pow5, pow4, pow3, pow2 = 6**k0, 5**k0, 4**k0, 3**k0, 2**k0
        for k in range(k0, limit+1):
            if isprime(pow6 - pow5 - pow4 - pow3 - pow2 - 1): print(k, end=", ")
            pow6 *= 6; pow5 *= 5; pow4 *= 4; pow3 *= 3; pow2 *= 2
    afind(1100) # Michael S. Branicky, Aug 21 2021

Extensions

a(11) from Michael S. Branicky, Aug 21 2021
a(12)-a(13) from Michael S. Branicky, Jul 05 2024
a(14) from Michael S. Branicky, May 24 2025
Showing 1-4 of 4 results.