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.

A180130 Smallest k such that k*2^n is a sum of two successive primes.

Original entry on oeis.org

5, 4, 2, 1, 7, 4, 2, 1, 9, 15, 8, 4, 2, 1, 25, 19, 11, 12, 6, 3, 10, 5, 35, 33, 52, 26, 13, 28, 14, 7, 15, 38, 19, 45, 47, 26, 13, 43, 84, 42, 21, 39, 35, 18, 9, 46, 23, 43, 49, 104, 52, 26, 13, 48, 24, 12, 6, 3, 21, 36, 18, 9, 15, 15, 9, 42, 21, 23, 67, 62, 31, 64, 32, 16, 8, 4, 2, 1, 45
Offset: 0

Views

Author

Zak Seidov & Robert G. Wilson v, Aug 15 2010

Keywords

Comments

If a(n) == 0 (mod 2), then a(n+1) = a(n)/2.
Records: 5, 7, 9, 15, 25, 35, 52, 84, 104, 146, 284, 330, 645, 660, 1020, 1677, 1701, 1747, 2247, 2991, ..., .
Corresponding primes are twin primes for n = 0, 1, 2, 3, 8, 17, 18, 19, 23, 43, 44, 64, 156, 189, 190, 210, 211, 212, 264, 265, 281, 282, 283, 388, 547, 725, 726, 727, ..., .

Links

Crossrefs

Cf. A180131, A180132, A180133, A180134, A179975, A180135, A180136, A180137, A180138.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, j = 2^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 79, 0]
  • Python
    from sympy import isprime, nextprime, prevprime
def ok(n):
  if n <= 5: return n == 5
  return not isprime(n//2) and n == prevprime(n//2) + nextprime(n//2)
def a(n):
  k, pow2 = 1, 2**n
  while not ok(k*pow2): k += 1
  return k
print([a(n) for n in range(79)]) # Michael S. Branicky, May 04 2021

A180131 Smallest k such that k*3^n is a sum of two successive primes.

Original entry on oeis.org

5, 4, 2, 6, 2, 10, 20, 26, 22, 10, 16, 8, 8, 72, 24, 8, 18, 6, 2, 6, 2, 10, 20, 20, 22, 20, 52, 50, 104, 118, 84, 28, 38, 306, 102, 34, 100, 50, 30, 10, 192, 64, 46, 66, 22, 220, 84, 28, 176, 88, 30, 10, 8, 152, 292, 98, 82, 124, 160, 206, 106, 106, 160, 128, 78, 26, 110, 80
Offset: 0

Views

Author

Zak Seidov & Robert G. Wilson v, Aug 15 2010

Keywords

Comments

If a(n) == 0 (mod 3), then a(n+1) = a(n)/3.
Records: 5, 6, 10, 20, 26, 72, 104, 118, 306, 320, 348, 572, 824, 828, 972, 1054, 1110, 1540, ..., .
Corresponding primes are twin primes for n = 0, 1, 10, 13, 14, 15, 22, 102, ..., .

Links

Crossrefs

Cf. A180130, A180132, A180133, A180134, A179975, A180135, A180136, A180137, A180138.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, j = 3^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 0]
  • Python
    from sympy import isprime, nextprime, prevprime
def ok(n):
  if n <= 5: return n == 5
  return not isprime(n//2) and n == prevprime(n//2) + nextprime(n//2)
def a(n):
  k, pow3 = 1, 3**n
  while not ok(k*pow3): k += 1
  return k
print([a(n) for n in range(68)]) # Michael S. Branicky, May 04 2021

A180132 Smallest k such that k*5^n is a sum of two successive primes.

Original entry on oeis.org

5, 1, 4, 10, 2, 8, 12, 12, 36, 12, 28, 66, 30, 6, 18, 132, 36, 108, 34, 14, 48, 60, 12, 22, 150, 30, 6, 74, 54, 16, 8, 66, 150, 30, 6, 14, 374, 110, 22, 82, 62, 66, 108, 348, 114, 428, 190, 38, 570, 114, 102, 24, 82, 86, 178, 420, 84, 108, 328, 186, 126, 192, 76, 82, 24
Offset: 0

Views

Author

Zak Seidov & Robert G. Wilson v, Aug 15 2010

Keywords

Comments

If a(n) == 0 (mod 5), then a(n+1) = a(n)/5.
Records: 5, 10, 12, 36, 66, 132, 150, 374, 428, 570, 734, 840, 1938, 2036, 2220, 2968, 3132, 3444, 4014, 6090, ..., .
Corresponding primes are twin primes for n = 0, 1, 51, 102, 103, 202, 275, ..., .

Links

Crossrefs

Cf. A180130, A180131, A180133, A180134, A179975, A180135, A180136, A180137, A180138.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, j = 5^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 0]
  • Python
    from sympy import nextprime, prevprime
def sum2succ(n): return n == prevprime(n//2) + nextprime(n//2)
def a(n):
  if n < 2: return [5, 1][n]
  k, pow5 = 1, 5**n
  while not sum2succ(k*pow5): k += 1
  return k
print([a(n) for n in range(65)]) # Michael S. Branicky, May 01 2021

A180133 Smallest k such that k*6^n is a sum of two successive primes.

Original entry on oeis.org

5, 2, 1, 1, 4, 12, 2, 1, 4, 3, 5, 8, 7, 34, 8, 11, 33, 26, 13, 9, 13, 90, 15, 40, 30, 5, 43, 9, 69, 38, 27, 79, 47, 9, 36, 6, 1, 92, 44, 51, 50, 16, 81, 21, 9, 50, 84, 14, 45, 59, 124, 215, 36, 6, 1, 20, 31, 35, 33, 46, 18, 3, 23, 114, 19, 41, 84, 14, 8, 35, 114, 19, 73, 14, 39, 68, 42
Offset: 0

Views

Author

Zak Seidov & Robert G. Wilson v, Aug 15 2010

Keywords

Comments

If a(n) == 0 (mod 6), then a(n+1) = a(n)/6.
Records: 5, 12, 34, 90, 92, 124, 215, 249, 592, 601, 1099, 1282, 1406, 1589, 1700, 2688, ..., .
Corresponding primes are twin primes for n = 0, 1, 2, 3, 4, 7, 13, 15, 28, 69, 120, 162, 251, 257, 279 ..., .

Links

Crossrefs

Cf. A180130, A180131, A180132, A180134, A179975, A180135, A180136, A180137, A180138.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, j = 6^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 0]
  • Python
    from sympy import nextprime, prevprime
def sum2succ(n): return n == prevprime(n//2) + nextprime(n//2)
def a(n):
  if n == 0: return 5
  k, pow6 = 1, 6**n
  while not sum2succ(k*pow6): k += 1
  return k
print([a(n) for n in range(77)]) # Michael S. Branicky, May 02 2021

A180134 Smallest k such that k*7^n is a sum of two successive primes.

Original entry on oeis.org

5, 6, 18, 10, 30, 18, 4, 28, 4, 30, 30, 60, 120, 38, 12, 6, 52, 120, 70, 10, 102, 60, 70, 10, 186, 174, 42, 6, 90, 146, 154, 22, 18, 140, 20, 168, 24, 240, 60, 80, 26, 286, 154, 22, 12, 196, 28, 4, 2, 128, 116, 156, 422, 130, 204, 84, 12, 118, 88, 240, 536, 564, 798, 114
Offset: 0

Views

Author

Zak Seidov & Robert G. Wilson v, Aug 15 2010

Keywords

Comments

If a(n) == 0 (mod 7), then a(n+1) = a(n)/7.
Records: 5, 6, 18, 30, 60, 120, 186, 240, 286, 422, 536, 564, 798, 1010, 1074, 1334, 1434, 1474, 3706, 4108, 4370, 6160, ..., .
Corresponding prime are twin primes for n = 0, 17, 369, ..., .

Links

Crossrefs

Cf. A180130, A180131, A180132, A180133, A179975, A180135, A180136, A180137, A180138.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, j = 7^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 0]
  • Python
    from sympy import isprime, nextprime, prevprime
def ok(n):
  if n <= 5: return n == 5
  return not isprime(n//2) and n == prevprime(n//2) + nextprime(n//2)
def a(n):
  k, pow7 = 1, 7**n
  while not ok(k*pow7): k += 1
  return k
print([a(n) for n in range(64)]) # Michael S. Branicky, May 06 2021

A180135 Smallest k such that k*11^n is a sum of two successive primes.

Original entry on oeis.org

5, 18, 6, 24, 6, 32, 40, 26, 20, 94, 50, 26, 10, 168, 30, 18, 196, 126, 70, 166, 30, 54, 130, 26, 50, 10, 40, 28, 20, 120, 84, 26, 228, 336, 92, 174, 24, 308, 28, 102, 216, 232, 68, 112, 192, 252, 512, 302, 110, 10, 330, 30, 138, 150, 168, 770, 70, 264, 24, 72, 180, 198
Offset: 0

Views

Author

Zak Seidov & Robert G. Wilson v, Aug 15 2010

Keywords

Comments

If a(n) == 0 (mod 11), then a(n+1) = a(n)/11.
Records: 5, 18, 24, 32, 40, 94, 168, 196, 228, 336, 512, 770, 996, 1446, 1644, 1812, 1900, 3840, ..., .
Corresponding primes are twin primes for n = 0, 3, ..., .

Links

Crossrefs

Cf. A180130, A180131, A180132, A180133, A180134, A179975, A180136, A180137, A180138.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, j = 11^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 0]
  • Python
    from sympy import isprime, nextprime, prevprime
def ok(n):
  if n <= 5: return n == 5
  return not isprime(n//2) and n == prevprime(n//2) + nextprime(n//2)
def a(n):
  k, pow11 = 1, 11**n
  while not ok(k*pow11): k += 1
  return k
print([a(n) for n in range(62)]) # Michael S. Branicky, May 18 2021

A180136 Smallest k such that k*12^n is a sum of two successive primes.

Original entry on oeis.org

5, 1, 1, 2, 18, 8, 13, 6, 2, 11, 11, 39, 20, 12, 1, 8, 9, 31, 182, 24, 2, 126, 128, 66, 9, 86, 146, 43, 170, 49, 155, 119, 115, 21, 77, 18, 60, 5, 119, 81, 27, 45, 81, 23, 28, 134, 14, 262, 131, 86, 55, 7, 549, 81, 199, 107, 100, 184, 85, 80, 32, 43, 118, 299, 43, 224, 187
Offset: 0

Views

Author

Zak Seidov & Robert G. Wilson v, Aug 15 2010

Keywords

Comments

If a(n) == 0 (mod 12), then a(n+1) = a(n)/12.
Records: 5, 18, 39, 182, 262, 549, 752, 811, 1456, ..., .
Corresponding primes are twin primes for n = 0, 1, 2, 5, 15, 26, 28, 55, 72, ..., .

Links

Crossrefs

Cf. A180130, A180131, A180132, A180133, A180134, A179975, A180135, A180137, A180138.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, j = 12^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 0]
  • Python
    from sympy import nextprime, prevprime
def sum2succ(n): return n == prevprime(n//2) + nextprime(n//2)
def a(n):
  if n == 0: return 5
  k, pow12 = 1, 12**n
  while not sum2succ(k*pow12): k += 1
  return k
print([a(n) for n in range(67)]) # Michael S. Branicky, May 01 2021

A180137 Smallest k such that k*13^n is a sum of two successive primes.

Original entry on oeis.org

5, 4, 24, 4, 8, 22, 40, 4, 14, 16, 28, 10, 266, 40, 20, 46, 112, 156, 12, 20, 228, 26, 2, 220, 60, 140, 92, 42, 316, 132, 84, 70, 68, 50, 280, 164, 112, 146, 148, 30, 36, 126, 390, 30, 30, 38, 462, 114, 14, 86, 56, 168, 1600, 224, 104, 8, 72, 434, 142, 60, 750, 202, 318
Offset: 0

Views

Author

Zak Seidov & Robert G. Wilson v, Aug 15 2010

Keywords

Comments

If a(n) == 0 (mod 13), then a(n+1) = a(n)/13.
Records: 5, 24, 40, 266, 316, 390, 462, 1600, 2616, 5834, ..., .
Corresponding primes are twin primes for n = 0, 2, ..., .

Links

Crossrefs

Cf. A180130, A180131, A180132, A180133, A180134, A179975, A180135, A180136, A180138.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, j = 13^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 0]
  • Python
    from sympy import isprime, nextprime, prevprime
def ok(n):
  if n <= 5: return n == 5
  return not isprime(n//2) and n == prevprime(n//2) + nextprime(n//2)
def a(n):
  k, pow13 = 1, 13**n
  while not ok(k*pow13): k += 1
  return k
print([a(n) for n in range(63)]) # Michael S. Branicky, May 04 2021
Showing 1-8 of 8 results.

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