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.

User: Soumadeep Ghosh

Soumadeep Ghosh's wiki page.

Soumadeep Ghosh has authored 5 sequences.

A269022 Primes p such that sigma(p)/pi(p) is prime.

Original entry on oeis.org

2, 3, 5, 7, 29, 349, 359, 3079, 70115921, 514274899, 514277977, 11091501632311
Offset: 1

Views

Author

Soumadeep Ghosh, Feb 17 2016

Keywords

Comments

Corresponding quotient primes are 3, 2, 2, 2, 3, 5, 5, 7, 17, 19, 19, 29.
a(13) > 8.1*10^13 if it exists. Assuming the Riemann Hypothesis, a(13) > 3.27*10^16 (if it exists). - Chai Wah Wu, May 25 2018

Examples

			7 is in the sequence because sigma(7) = 8, pi(7) = 4 and 8/4 = 2 is a prime.

Crossrefs

Subsequence of A052013.
Cf. A000203, A000720.

Programs

  • Mathematica
    Select[Prime[Range[10^6]], ProvablePrimeQ[DivisorSigma[1, #]/PrimePi[#]] &]
Select[ (* the terms of A052013 *), PrimeQ[(# + 1)/PrimePi@ #] &] (* Robert G. Wilson v, Mar 16 2016 *)
  • PARI
    is(n)=my(t=(n+1)/primepi(n)); denominator(t)==1 && isprime(t) && isprime(n) \\ Charles R Greathouse IV, Feb 18 2016
  • PARI
    list(lim)=my(v=List(),n,t); forprime(p=2,lim, t=(p+1)/n++; if(denominator(t)==1 && isprime(t), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 18 2016

Extensions

a(9)-a(11) from Charles R Greathouse IV, Feb 18 2016
a(12) from Chai Wah Wu, May 25 2018

A268987 Primes of the form k^(k + 1) + k - 1.

Original entry on oeis.org

83, 15629, 279941, 3486784409, 6568408355712890639
Offset: 1

Views

Author

Soumadeep Ghosh, Feb 16 2016

Keywords

Comments

The next prime has 171 digits. - Vincenzo Librandi, Feb 17 2016
Subsequence of primes of A155499. - Michel Marcus, Feb 20 2016

Links

Crossrefs

Cf. A155499, A161471, A161472, A187602, A187605.
Cf. A309140 (the corresponding values of k).

Programs

  • Magma
    [a: n in [0..100] | IsPrime(a) where a is n^(n+1)+n-1]; // Vincenzo Librandi, Feb 17 2016
  • Mathematica
    Select[Table[n^(n + 1) + n - 1, {n, 1, 50}], ProvablePrimeQ[#] &]
  • PARI
    lista(nn) = for(k=1, nn, if(ispseudoprime(q=k^(k+1)+k-1), print1(q, ", "))); \\ Jinyuan Wang, Mar 01 2020

A268860 Prime numbers ending in 27.

Original entry on oeis.org

127, 227, 727, 827, 1327, 1427, 1627, 2027, 2927, 3527, 3727, 4027, 4127, 4327, 5227, 5527, 5827, 5927, 6427, 6827, 7027, 7127, 7727, 7927, 8527, 8627, 9127, 9227, 10427, 10627, 11027, 11527, 11827, 11927, 12227, 12527, 13127, 13327, 13627, 14327, 14627
Offset: 1

Views

Author

Soumadeep Ghosh, Feb 14 2016

Keywords

Crossrefs

Cf. A268858, A268859.

Programs

  • Magma
    [n: n in PrimesUpTo(15000) | n mod 100 eq 27]; // Vincenzo Librandi, Feb 15 2016
  • Maple
    A268860:=n->`if`(isprime(n) and n mod 100 = 27, n, NULL): seq(A268860(n), n=1..5*10^4); # Wesley Ivan Hurt, Apr 02 2016
  • Mathematica
    Select[Table[27 + 100 i, {i, 0, 10^3}], ProvablePrimeQ[#] &]
  • PARI
    lista(nn) = {forprime(p=2, nn, if ((p-27) % 100 == 0, print1(p, ", ")););} \\ Michel Marcus, Feb 20 2016
  • Python
    from sympy import isprime
for n in range(127,10000,100):
    if(isprime(n)):print(n)
# Soumil Mandal, Apr 02 2016

A268859 Prime numbers ending in 21.

Original entry on oeis.org

421, 521, 821, 1021, 1321, 1621, 1721, 2221, 2521, 2621, 3121, 3221, 3821, 4021, 4421, 4621, 4721, 5021, 5521, 5821, 6121, 6221, 6421, 6521, 7121, 7321, 7621, 8221, 8521, 8821, 9221, 9421, 9521, 9721, 10321, 11321, 11621, 11821, 12421, 12721, 12821, 13121
Offset: 1

Views

Author

Soumadeep Ghosh, Feb 14 2016

Keywords

Crossrefs

Cf. A268858, A268860.

Programs

  • Magma
    [n: n in PrimesUpTo(15000) | n mod 100 eq 21]; // Vincenzo Librandi, Feb 15 2016
  • Maple
    A268859:=n->`if`(isprime(n) and n mod 100 = 21, n, NULL): seq(A268859(n), n=1..5*10^4); # Wesley Ivan Hurt, Apr 02 2016
  • Mathematica
    Select[Table[21 + 100 i, {i, 0, 10^3}], ProvablePrimeQ[#] &]
  • PARI
    lista(nn) = {for(n=1, nn, if (isprime(p=100*n+21), print1(p, ", ")););} \\ Michel Marcus, Feb 20 2016
  • Python
    from sympy import isprime
for n in range(421,15000,100):
    if(isprime(n)):print(n)
# Soumil Mandal, Apr 03 2016

A268858 Prime numbers ending in 39.

Original entry on oeis.org

139, 239, 439, 739, 839, 1039, 1439, 2039, 2239, 2339, 2539, 2939, 3539, 3739, 4139, 4339, 4639, 5039, 5639, 5839, 5939, 7039, 7639, 8039, 8539, 8839, 9239, 9439, 9539, 9739, 9839, 10039, 10139, 10639, 10739, 10939, 11239, 11839, 11939, 12239, 12539, 12739
Offset: 1

Views

Author

Soumadeep Ghosh, Feb 14 2016

Keywords

Links

Crossrefs

Cf. A268859, A268860.

Programs

  • Magma
    [n: n in PrimesUpTo(15000) | n mod 100 eq 39]; // Vincenzo Librandi, Feb 15 2016
  • Maple
    A268858:=n->`if`(isprime(n) and n mod 100 = 39, n, NULL): seq(A268858(n), n=1..4*10^4); # Wesley Ivan Hurt, Apr 02 2016
  • Mathematica
    Select[Table[39 + 100 i, {i, 0, 10^3}], ProvablePrimeQ[#] &]
  • PARI
    lista(nn) = {for(n=1, nn, if (isprime(p=100*n+39), print1(p, ", ")););} \\ Michel Marcus, Feb 20 2016
  • Python
    from sympy import isprime
for n in range(139,15000,100):
    if(isprime(n)):print(n)
# Soumil Mandal, Apr 03 2016

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