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 1-9 of 9 results.

A088420 Number of primes in arithmetic progression starting with 3 and with d = 2n.

Original entry on oeis.org

3, 3, 1, 3, 3, 1, 3, 2, 1, 3, 1, 1, 2, 3, 1, 1, 3, 1, 3, 3, 1, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 1, 3, 2, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 3, 1, 3, 2, 1, 3, 2, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 2, 2, 1, 1, 3, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 3, 3, 1, 2, 2, 1, 1
Offset: 1

Views

Author

Zak Seidov, Sep 29 2003

Keywords

Comments

The arithmetic progression is stopped when the next term is not prime. E.g., for n=5, a=3, the numbers 3, 13, and 23 are prime, while the next term, 33, is not prime.
a(n) <= 3 because 3+3*d is divisible by 3. - Klaus Brockhaus, May 14 2009

Crossrefs

Cf. A088421, A088422, A088423, A088424, A088425, A088426, A088427, A088428, A088429.
Cf. A115334. - Klaus Brockhaus, May 14 2009

Programs

  • Magma
    npap3:=function(d) c:=1; p:=3+d; while IsPrime(p) do c+:=1; p+:=d; end while; return c; end function; [ npap3(2*n): n in [1..105] ]; // Klaus Brockhaus, May 14 2009

A088423 a(n) is the number of primes in arithmetic progression starting with 11 and with d = 2n.

Original entry on oeis.org

2, 1, 4, 2, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 5, 2, 1, 3, 1, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 6, 2, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 1, 2, 1, 4, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 4, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 2, 2, 1, 4, 2, 1, 1, 1, 1, 1, 2
Offset: 1

Views

Author

Zak Seidov, Sep 29 2003

Keywords

Comments

Arithmetic progression is stopped when next term is not prime. E.g., for n=3, a=4, that is 11,17,23,29 are prime, while next term, 35, is not prime.

Links

Crossrefs

Cf. A088420, A088421, A088422, A088424, A088425, A088426, A088427, A088428, A088429.

Programs

  • Mathematica
    bb={}; Do[s=1; Do[If[PrimeQ[11+k*d], s=s+1, bb={bb, s}; Break[]], {k, 10}], {d, 2, 200, 2}]; Flatten[bb]
  • PARI
    a(n) = my(p=11, x=p+2*n, i=1); while(1, if(ispseudoprime(x), i++; x=x+2*n, return(i))) \\ Felix Fröhlich, May 28 2021

A088426 Number of primes in arithmetic progression starting with 19 and with d=2n.

Original entry on oeis.org

1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 2, 4, 1, 1, 4, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 3, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 4, 1, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1
Offset: 1

Views

Author

Zak Seidov, Sep 29 2003

Keywords

Comments

Arithmetic progression is stopped when next term is not prime. E.g. for n=6 (d=12), a=3, that is 19,31,43 are prime, while next term, 55, is not prime.
From Robert Israel, Jul 27 2020: (Start)
a(n) = 1 if n == 1 (mod 3), a(n) <= 2 if n == 2 (mod 3).
If a(n) >= p where p is 3, 5, 7, 11, 13 or 17, then n is divisible by p.
All a(n) < 19.
Records:
a(1)=1
a(2)=2
a(6)=3
a(27)=4
a(210)=5
a(825)=6
a(16380)=7
a(273420)=9
a(17853675)=10 (End)
From David A. Corneth, Jul 29 2020: (Start)
Other first occurrences are:
a(779520) = 8
a(4918073160) = 11
a(3187366788375) = 12
a(6125952702870) = 13
If a(k) = 14 then k > 4.8*10^15.
If a(k) = 15 then k > 1.77 * 10^16. (End)

Links

Crossrefs

Cf. A005115, A088420, A088421, A088422, A088423, A088424, A088425, A088427, A088428, A088429.

Programs

  • Maple
    f:= proc(n) local d,k;
  d:= 2*n;
  for k from 1 while isprime(19+d*k) do od:
  k
end proc:
map(f, [$1..200]); # Robert Israel, Jul 27 2020
  • Mathematica
    bb={}; Do[s=1; Do[If[PrimeQ[19+k*d], s=s+1, bb={bb, s}; Break[]], {k, 10}], {d, 2, 200, 2}]; Flatten[bb]

A088421 Number of primes in arithmetic progression starting with 5 and with d=2n.

Original entry on oeis.org

2, 1, 5, 2, 1, 5, 2, 1, 4, 1, 1, 3, 2, 1, 1, 2, 1, 2, 2, 1, 5, 1, 1, 5, 1, 1, 4, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 1, 2, 1, 1, 4, 1, 1, 1, 2, 1, 5, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 5, 1, 1, 4, 2, 1, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 2, 2, 1, 3, 2, 1, 1, 1
Offset: 1

Views

Author

Zak Seidov, Sep 29 2003

Keywords

Comments

Arithmetic progression is stopped when next term is not prime. E.g. for n=3, a=5, that is 5,11,17,23,29 are prime, while next term, 35, is not prime.

Crossrefs

Cf. A088420, A088422, A088423, A088424, A088425, A088426, A088427, A088428, A088429.

Programs

  • Mathematica
    bb={}; Do[s=1; Do[If[PrimeQ[5+k*d], s=s+1, bb={bb, s}; Break[]], {k, 10}], {d, 2, 200, 2}]; Flatten[bb]

A088424 Number of primes in arithmetic progression starting with 13 and with d=2n.

Original entry on oeis.org

1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 3, 1, 2, 4, 1, 2, 1, 1, 2, 1, 1, 2, 4, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 2, 6, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 5, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 2, 3, 1, 2, 2, 1, 1, 1, 1, 1, 4, 1
Offset: 1

Views

Author

Zak Seidov, Sep 29 2003

Keywords

Comments

Arithmetic progression is stopped when next term is not prime. E.g. for n=15, a=4, that is 13,43,73,103 are prime, while next term, 133, is not prime.

Crossrefs

Cf. A088420, A088421, A088422, A088423, A088425, A088426, A088427, A088428, A088429.

Programs

  • Mathematica
    bb={}; Do[s=1; Do[If[PrimeQ[13+k*d], s=s+1, bb={bb, s}; Break[]], {k, 10}], {d, 2, 200, 2}]; Flatten[bb]

A088425 Number of primes in arithmetic progression starting with 17 and with d=2n.

Original entry on oeis.org

2, 1, 3, 1, 1, 4, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 3, 1, 1, 3, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 3, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 2, 1, 5, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1
Offset: 1

Views

Author

Zak Seidov, Sep 29 2003

Keywords

Comments

Arithmetic progression is stopped when next term is not prime. E.g. for n=6 (d=12), a=4, that is 17,29,41,53 are prime, while next term, 65, is not prime.

Crossrefs

Cf. A088420, A088421, A088422, A088423, A088424, A088426, A088427, A088428, A088429.

Programs

  • Mathematica
    bb={}; Do[s=1; Do[If[PrimeQ[17+k*d], s=s+1, bb={bb, s}; Break[]], {k, 10}], {d, 2, 200, 2}]; Flatten[bb]

A088427 Number of primes in arithmetic progression starting with 23 and with d=2n.

Original entry on oeis.org

1, 1, 2, 2, 1, 1, 2, 1, 3, 2, 1, 3, 1, 1, 4, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 4, 2, 1, 3, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 3, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 3, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2
Offset: 1

Views

Author

Zak Seidov, Sep 29 2003

Keywords

Comments

Arithmetic progression is stopped when next term is not prime. E.g. for n=15 (d=30), a=3, that is 23,53,83,113 are prime, while next term, 143, is not prime.

Crossrefs

Cf. A088420, A088421, A088422, A088423, A088424, A088425, A088426, A088428, A088429.

Programs

  • Mathematica
    bb={}; Do[s=1; Do[If[PrimeQ[23+k*d], s=s+1, bb={bb, s}; Break[]], {k, 10}], {d, 2, 200, 2}]; Flatten[bb]

A088428 Number of primes in arithmetic progression starting with 29 and with d=2n.

Original entry on oeis.org

2, 1, 1, 2, 1, 3, 2, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 1, 4, 1, 1, 3, 1, 1, 1, 2, 1, 3, 2, 1, 2, 2, 1, 4, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 5, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 1, 3, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2
Offset: 1

Views

Author

Zak Seidov, Sep 29 2003

Keywords

Comments

Arithmetic progression is stopped when next term is not prime. E.g. for n=6 (d=12), a=3, that is 29,41,53 are prime, while next term, 65, is not prime.

Crossrefs

Cf. A088420, A088421, A088422, A088423, A088424, A088425, A088426, A088427, A088429.

Programs

  • Mathematica
    bb={}; Do[s=1; Do[If[PrimeQ[29+k*d], s=s+1, bb={bb, s}; Break[]], {k, 10}], {d, 2, 200, 2}]; Flatten[bb]

A088429 Number of primes in arithmetic progression starting with 31 and with d=2n.

Original entry on oeis.org

1, 1, 3, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 4, 1, 2, 2, 1, 1, 3, 1, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 1, 1, 4, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 2, 2, 1, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1
Offset: 1

Views

Author

Zak Seidov, Sep 29 2003

Keywords

Comments

Arithmetic progression is stopped when next term is not prime. E.g. for n=3 (d=6), a=3, that is 31,37,43 are prime, while next term, 49, is not prime.

Crossrefs

Cf. A088420, A088421, A088422, A088423, A088424, A088425, A088426, A088427, A088428.

Programs

  • Mathematica
    bb={}; Do[s=1; Do[If[PrimeQ[31+k*d], s=s+1, bb={bb, s}; Break[]], {k, 10}], {d, 2, 200, 2}]; Flatten[bb]
Showing 1-9 of 9 results.

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