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 1-8 of 8 results.

A332179 a(n) = 7*(10^(2n+1)-1)/9 + 2*10^n.

Original entry on oeis.org

9, 797, 77977, 7779777, 777797777, 77777977777, 7777779777777, 777777797777777, 77777777977777777, 7777777779777777777, 777777777797777777777, 77777777777977777777777, 7777777777779777777777777, 777777777777797777777777777, 77777777777777977777777777777, 7777777777777779777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Comments

See A183183 = {1, 2, 8, 19, 20, 212, 280, ...} for the indices of primes.

Links

Crossrefs

Cf. A138148 (cyclops numbers with binary digits only).
Cf. (A077796-1)/2 = A183183: indices of primes.
Cf. A002275 (repunits R_n = [10^n/9]), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332178 (variants with different middle digit 1, ..., 8).

Programs

  • Maple
    A332179 := n -> 7*(10^(n*2+1)-1)/9 + 2*10^n;
  • Mathematica
    Array[7 (10^(2 # + 1) - 1)/9 + 2*10^# &, 15, 0]
  • PARI
    apply( {A332179(n)=10^(n*2+1)\9*7+2*10^n}, [0..15])
  • Python
    def A332179(n): return 10**(n*2+1)//9*7+2*10^n

Formula

a(n) = 7*A138148(n) + 9*10^n.
G.f.: (9 - 202*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.

A332178 a(n) = 7*(10^(2n+1)-1)/9 + 10^n.

Original entry on oeis.org

8, 787, 77877, 7778777, 777787777, 77777877777, 7777778777777, 777777787777777, 77777777877777777, 7777777778777777777, 777777777787777777777, 77777777777877777777777, 7777777777778777777777777, 777777777777787777777777777, 77777777777777877777777777777, 7777777777777778777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Comments

See A183182 = {1, 3, 39, 54, 168, 240, ...} for the indices of primes.

Links

Crossrefs

Cf. A138148 (cyclops numbers with binary digits only).
Cf. (A077793-1)/2 = A183182: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332178 := n -> 7*(10^(n*2+1)-1)/9 + 10^n;
  • Mathematica
    Array[7 (10^(2 # + 1) - 1)/9 + 10^# &, 15, 0]
  • PARI
    apply( {A332178(n)=10^(n*2+1)\9*7+10^n}, [0..15])
  • Python
    def A332178(n): return 10**(n*2+1)//9*7+10^n

Formula

a(n) = 7*A138148(n) + 8*10^n.
G.f.: (8 - 101*x - 600*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.

A332170 a(n) = 7*(10^(2n+1)-1)/9 - 7*10^n.

Original entry on oeis.org

0, 707, 77077, 7770777, 777707777, 77777077777, 7777770777777, 777777707777777, 77777777077777777, 7777777770777777777, 777777777707777777777, 77777777777077777777777, 7777777777770777777777777, 777777777777707777777777777, 77777777777777077777777777777, 7777777777777770777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Links

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
Cf. A332120 .. A332190 (variants with different repeated digit 2, ..., 9).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332170 := n -> 7*(10^(2*n+1)-1)/9-7*10^n;
  • Mathematica
    Array[7 ((10^(2 # + 1)-1)/9 - 10^#) &, 15, 0]
  • PARI
    apply( {A332170(n)=(10^(n*2+1)\9-10^n)*7}, [0..15])
  • Python
    def A332170(n): return (10**(n*2+1)//9-10^n)*7

Formula

a(n) = 7*A138148(n) = A002281(2n+1) - 7*A011557(n).
G.f.: 7*x*(101 - 200*x)/((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.

A332172 a(n) = 7*(10^(2n+1)-1)/9 - 5*10^n.

Original entry on oeis.org

2, 727, 77277, 7772777, 777727777, 77777277777, 7777772777777, 777777727777777, 77777777277777777, 7777777772777777777, 777777777727777777777, 77777777777277777777777, 7777777777772777777777777, 777777777777727777777777777, 77777777777777277777777777777, 7777777777777772777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 06 2020

Keywords

Comments

Indices of prime terms: {0, 1, 3, 7, 10, 12, 480, 949, ...} = A183178.

Links

Crossrefs

Cf. A138148 (cyclops numbers with binary digits only).
Cf. A332171 (analog with middle digit 1).
Cf. (A077777-1)/2 = A183178: indices of primes.
Cf. A002275 (repunits R_n = [10^n/9]), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332172 := n -> 7*(10^(n*2+1)-1)/9 -5*10^n;
  • Mathematica
    Array[7 (10^(2 # +1)-1)/9 -5*10^# &, 15, 0]
  • PARI
    apply( {A332172(n)=10^(n*2+1)\9*7-5*10^n}, [0..25])
  • Python
    def A332172(n): return 10**(n*2+1)//9*7-5*10^n

Formula

a(n) = 7*A138148(n) + 2*10^n.
G.f.: (2 + 505*x - 1200*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.

A332173 a(n) = 7*(10^(2n+1)-1)/9 - 4*10^n.

Original entry on oeis.org

3, 737, 77377, 7773777, 777737777, 77777377777, 7777773777777, 777777737777777, 77777777377777777, 7777777773777777777, 777777777737777777777, 77777777777377777777777, 7777777777773777777777777, 777777777777737777777777777, 77777777777777377777777777777, 7777777777777773777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 06 2020

Keywords

Comments

According to M. Kamada, n = 0 and n = 2 are the only indices of a prime up to n = 2*10^4.

Links

Crossrefs

Cf. A138148 (cyclops numbers with binary digits only).
Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332173 := n -> 7*(10^(n*2+1)-1)/9 - 4*10^n;
  • Mathematica
    Array[7 (10^(2 # + 1) - 1)/9 - 4*10^# &, 15, 0]
  • PARI
    apply( {A332173(n)=10^(n*2+1)\9*7-4*10^n}, [0..15])
  • Python
    def A332173(n): return 10**(n*2+1)//9*7-4*10^n

Formula

a(n) = 7*A138148(n) + 3*10^n.
G.f.: (1 + 404*x - 1100*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.
E.g.f.: exp(x)*(70*exp(99*x) - 36*exp(9*x) - 7)/9. - Stefano Spezia, Feb 19 2025

A332174 a(n) = 7*(10^(2n+1)-1)/9 - 3*10^n.

Original entry on oeis.org

4, 747, 77477, 7774777, 777747777, 77777477777, 7777774777777, 777777747777777, 77777777477777777, 7777777774777777777, 777777777747777777777, 77777777777477777777777, 7777777777774777777777777, 777777777777747777777777777, 77777777777777477777777777777, 7777777777777774777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Comments

See A183179 = {2, 3, 6, 23, 36, 69, 561, ...} for the indices of primes.

Links

Crossrefs

Cf. A138148 (cyclops numbers with binary digits only).
Cf. (A077781-1)/2 = A183179: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332174 := n -> 7*(10^(n*2+1)-1)/9 - 3*10^n;
  • Mathematica
    Array[7 (10^(2 # + 1) - 1)/9 - 3*10^# &, 15, 0]
  • PARI
    apply( {A332174(n)=10^(n*2+1)\9*7-3*10^n}, [0..15])
  • Python
    def A332174(n): return 10**(n*2+1)//9*7-3*10^n

Formula

a(n) = 7*A138148(n) + 4*10^n.
G.f.: (4 + 303*x - 1000*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.
E.g.f.: (1/9)*exp(x)*(70*exp(99*x) - 27*exp(9*x) - 7). - Stefano Spezia, Feb 08 2020

A332175 a(n) = 7*(10^(2n+1)-1)/9 - 2*10^n.

Original entry on oeis.org

5, 757, 77577, 7775777, 777757777, 77777577777, 7777775777777, 777777757777777, 77777777577777777, 7777777775777777777, 777777777757777777777, 77777777777577777777777, 7777777777775777777777777, 777777777777757777777777777, 77777777777777577777777777777, 7777777777777775777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Comments

See A183180 = {0, 1, 7, 13, 58, 129, 253, ...} for the indices of primes.

Links

Crossrefs

Cf. (A077785-1)/2 = A183180: indices of primes.
Cf. A138148 (cyclops numbers with binary digits only).
Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332175 := n -> 7*(10^(n*2+1)-1)/9 - 2*10^n;
  • Mathematica
    Array[7 (10^(2 # + 1) - 1)/9 - 2*10^# &, 15, 0]
  • PARI
    apply( {A332175(n)=10^(n*2+1)\9*7-2*10^n}, [0..15])
  • Python
    def A332175(n): return 10**(n*2+1)//9*7-2*10^n

Formula

a(n) = 7*A138148(n) + 5*10^n.
G.f.: (5 + 202*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.
E.g.f.: (1/9)*exp(x)*(70*exp(99*x) - 18*exp(9*x) - 7). - Stefano Spezia, Feb 08 2020

A332176 a(n) = 7*(10^(2n+1)-1)/9 - 10^n.

Original entry on oeis.org

6, 767, 77677, 7776777, 777767777, 77777677777, 7777776777777, 777777767777777, 77777777677777777, 7777777776777777777, 777777777767777777777, 77777777777677777777777, 7777777777776777777777777, 777777777777767777777777777, 77777777777777677777777777777, 7777777777777776777777777777777
Offset: 0

Views

Author

M. F. Hasler, Feb 08 2020

Keywords

Comments

See A183181 = {4, 5, 8, 11, 1244, 1685, ...} for the indices of primes.

Links

Crossrefs

Cf. A138148 (cyclops numbers with binary digits only).
Cf. (A077788-1)/2 = A183181: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

Programs

  • Maple
    A332176 := n -> 7*(10^(n*2+1)-1)/9 - 10^n;
  • Mathematica
    Array[7 (10^(2 # + 1) - 1)/9 - 10^# &, 15, 0]
  • PARI
    apply( {A332176(n)=10^(n*2+1)\9*7-10^n}, [0..15])
  • Python
    def A332176(n): return 10**(n*2+1)//9*7-10^n

Formula

a(n) = 7*A138148(n) + 6*10^n.
G.f.: (6 + 101*x - 800*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.
Showing 1-8 of 8 results.

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