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.

Previous Showing 11-15 of 15 results.

A332187 a(n) = 8*(10^(2n+1)-1)/9 - 10^n.

Original entry on oeis.org

7, 878, 88788, 8887888, 888878888, 88888788888, 8888887888888, 888888878888888, 88888888788888888, 8888888887888888888, 888888888878888888888, 88888888888788888888888, 8888888888887888888888888, 888888888888878888888888888, 88888888888888788888888888888, 8888888888888887888888888888888
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Links

Crossrefs

Cf. (A077776-1)/2 = A183190: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A002282 (8*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
Cf. A332117 .. A332197 (variants with different "wing" digit 1, ..., 9).
Cf. A332180 .. A332189 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332187 := n -> 8*(10^(2*n+1)-1)/9-10^n;
  • Mathematica
    Array[8 (10^(2 # + 1)-1)/9 - 10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{7,878,88788},20] (* Harvey P. Dale, Jul 21 2024 *)
  • PARI
    apply( {A332187(n)=10^(n*2+1)\9*8-10^n}, [0..15])
  • Python
    def A332187(n): return 10**(n*2+1)//9*8-10**n

Formula

a(n) = 8*A138148(n) + 7*10^n = A002282(2n+1) - 10^n.
G.f.: (7 + 101*x - 900*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332167 a(n) = 6*(10^(2*n+1)-1)/9 + 10^n.

Original entry on oeis.org

7, 676, 66766, 6667666, 666676666, 66666766666, 6666667666666, 666666676666666, 66666666766666666, 6666666667666666666, 666666666676666666666, 66666666666766666666666, 6666666666667666666666666, 666666666666676666666666666, 66666666666666766666666666666, 6666666666666667666666666666666
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002280 (6*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332117 .. A332197 (variants with different repeated digit 1, ..., 9).
Cf. A332160 .. A332169 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332167 := n -> 6*(10^(2*n+1)-1)/9+10^n;
  • Mathematica
    Array[6 (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]
  • PARI
    apply( {A332167(n)=10^(n*2+1)\9*6+10^n}, [0..15])
  • Python
    def A332167(n): return 10**(n*2+1)//9*6+10**n

Formula

a(n) = 6*A138148(n) + 7*10^n = A002280(2n+1) + 10^n.
G.f.: (7 - 101*x - 500*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332137 a(n) = (10^(2n+1)-1)/3 + 4*10^n.

Original entry on oeis.org

7, 373, 33733, 3337333, 333373333, 33333733333, 3333337333333, 333333373333333, 33333333733333333, 3333333337333333333, 333333333373333333333, 33333333333733333333333, 3333333333337333333333333, 333333333333373333333333333, 33333333333333733333333333333, 3333333333333337333333333333333
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Comments

See A183176 = {1, 3, 7, 11, 13, 17, 29, 31, ...} for the indices of primes.

Links

Crossrefs

Cf. (A077790-1)/2 = A183176: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A002277 (3*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332127 .. A332197 (variants with different repeated digit 2, ..., 9).
Cf. A332130 .. A332139 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332137 := n -> (10^(2*n+1)-1)/3+4*10^n;
  • Mathematica
    Array[ (10^(2 # + 1)-1)/3 + 4*10^# &, 15, 0]
  • PARI
    apply( {A332137(n)=10^(n*2+1)\3+4*10^n}, [0..15])
  • Python
    def A332137(n): return 10**(n*2+1)//3+4*10**n

Formula

a(n) = 3*A138148(n) + 7*10^n = A002277(2n+1) + 4*10^n.
G.f.: (7 - 404*x + 100*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332147 a(n) = 4*(10^(2*n+1)-1)/9 + 3*10^n.

Original entry on oeis.org

7, 474, 44744, 4447444, 444474444, 44444744444, 4444447444444, 444444474444444, 44444444744444444, 4444444447444444444, 444444444474444444444, 44444444444744444444444, 4444444444447444444444444, 444444444444474444444444444, 44444444444444744444444444444, 4444444444444447444444444444444
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002278 (4*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332117 .. A332197 (variants with different repeated digit 1, ..., 9).
Cf. A332140 .. A332149 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332147 := n -> 4*(10^(2*n+1)-1)/9+3*10^n;
  • Mathematica
    Array[4 (10^(2 # + 1)-1)/9 + 3*10^# &, 15, 0]
LinearRecurrence[{111,-1110,1000},{7,474,44744},20] (* Harvey P. Dale, Mar 08 2022 *)
  • PARI
    apply( {A332147(n)=10^(n*2+1)\9*4+3*10^n}, [0..15])
  • Python
    def A332147(n): return 10**(n*2+1)//9*4+3*10**n

Formula

a(n) = 4*A138148(n) + 7*10^n = A002278(2n+1) + 3*10^n.
G.f.: (7 - 303*x - 100*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A332157 a(n) = 5*(10^(2*n+1)-1)/9 + 2*10^n.

Original entry on oeis.org

7, 575, 55755, 5557555, 555575555, 55555755555, 5555557555555, 555555575555555, 55555555755555555, 5555555557555555555, 555555555575555555555, 55555555555755555555555, 5555555555557555555555555, 555555555555575555555555555, 55555555555555755555555555555, 5555555555555557555555555555555
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002279 (5*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332117 .. A332197 (variants with different repeated digit 1, ..., 9).
Cf. A332150 .. A332159 (variants with different middle digit 0, ..., 9).

Programs

  • Maple
    A332157 := n -> 5*(10^(2*n+1)-1)/9+2*10^n;
  • Mathematica
    Array[5 (10^(2 # + 1)-1)/9 + 2*10^# &, 15, 0]
  • PARI
    apply( {A332157(n)=10^(n*2+1)\9*5+2*10^n}, [0..15])
  • Python
    def A332157(n): return 10**(n*2+1)//9*5+2*10**n

Formula

a(n) = 5*A138148(n) + 7*10^n = A002279(2n+1) + 2*10^n.
G.f.: (7 - 202*x - 300*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.
Previous Showing 11-15 of 15 results.

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

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