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.

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A204902 Least prime p such that n divides p-q for some odd prime q

Original entry on oeis.org

5, 5, 11, 7, 13, 11, 17, 11, 23, 13, 29, 17, 29, 17, 37, 19, 37, 23, 41, 23, 47, 29, 53, 29, 53, 29, 59, 31, 61, 37, 67, 37, 71, 37, 73, 41, 79, 41, 83, 43, 89, 47, 89, 47, 97, 53, 97, 53, 101, 53, 107, 59, 109, 59, 113, 59, 127, 61, 131, 67, 127, 67, 131, 67
Offset: 1

Views

Author

Clark Kimberling, Jan 20 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A204900, A204892.

Programs

  • Mathematica
    (See the program at A204900.)

A204906 Ordered differences of primes >=5.

Original entry on oeis.org

2, 6, 4, 8, 6, 2, 12, 10, 6, 4, 14, 12, 8, 6, 2, 18, 16, 12, 10, 6, 4, 24, 22, 18, 16, 12, 10, 6, 26, 24, 20, 18, 14, 12, 8, 2, 32, 30, 26, 24, 20, 18, 14, 8, 6, 36, 34, 30, 28, 24, 22, 18, 12, 10, 4, 38, 36, 32, 30, 26, 24, 20, 14, 12, 6, 2, 42, 40, 36, 34, 30, 28, 24
Offset: 1

Views

Author

Clark Kimberling, Jan 20 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Examples

			Ordering (as at A204892):
s(2)-s(1)=7-5=2
s(3)-s(1)=11-5=6
s(3)-s(2)=11-7=4
s(4)-s(1)=13-5=8
s(4)-s(2)=13-7=6

Crossrefs

Cf. A204908, A204900, A204892.

Programs

  • Mathematica
    (See the program at A204908.)

A204909 The index jA204908) for which such j exists.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jan 20 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A204908, A204900, A204892.

Programs

  • Mathematica
    (See the program at A204908.)

A204919 a(n) = q^2 where q is the least prime such that n divides A204916(n)^2 - q^2.

Original entry on oeis.org

4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 25, 4, 9, 4, 9, 4, 49, 4, 9, 4, 25, 289, 25, 4, 49, 4, 9, 4, 49, 4, 25, 4, 121, 9, 49, 961, 49, 4, 9, 4, 121, 4, 25, 4, 289, 1681, 25, 4, 361, 4, 49, 2209, 529, 4, 9, 4, 289, 4, 49
Offset: 1

Views

Author

Clark Kimberling, Jan 20 2012

Keywords

Comments

For a guide to related sequences, see A204892.
Original name was "Least prime q^2 such that n divides p^2-q^2 for some prime p>q", which would be A089090. - Robert Israel, May 04 2019

Links

Crossrefs

Cf. A089090, A204916, A204908, A204900, A204892.

Programs

  • Maple
    N:= 100: # to get a(1)..a(N)
A:= Vector(N): count:= 0:
p:= 2: P:= 2:
for i from 1 while count < N do
  p:= nextprime(p);
  ps:= p^2;
  P:= P, p;
  for j from 1 to i while count < N do
   qs:= P[j]^2;
   S:= convert(select(t -> t <= N and A[t]=0, numtheory:-divisors(ps-qs)),list);
   A[S]:= qs;
   count:= count + nops(S);
od od:
convert(A,list); # Robert Israel, May 04 2019
  • Mathematica
    (See the program at A204916.)

Extensions

Name corrected by Robert Israel, May 04 2019

A204899 Least k such that n divides A204898(k), the k-th difference of two odd primes.

Original entry on oeis.org

1, 1, 5, 2, 7, 5, 11, 4, 23, 7, 31, 12, 29, 11, 48, 16, 46, 23, 56, 22, 80, 31, 94, 30, 92, 29, 107, 37, 121, 48, 138, 47, 155, 46, 172, 57, 192, 56, 212, 67, 234, 80, 232, 79, 256, 94, 254, 93, 277, 92
Offset: 1

Views

Author

Clark Kimberling, Jan 20 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A204900, A204892.

Programs

  • Mathematica
    (See the program at A204900.)

A204904 p(n)-q(n), where (p(n), q(n)) is the least pair of odd primes for which n divides p(n)-q(n).

Original entry on oeis.org

2, 2, 6, 4, 10, 6, 14, 8, 18, 10, 22, 12, 26, 14, 30, 16, 34, 18, 38, 20, 42, 22, 46, 24, 50, 26, 54, 28, 58, 30, 62, 32, 66, 34, 70, 36, 74, 38, 78, 40, 82, 42, 86, 44, 90, 46, 94, 48, 98, 50, 102, 52, 106, 54, 110, 56, 114, 58, 118, 60, 122, 62, 126, 64, 130
Offset: 1

Views

Author

Clark Kimberling, Jan 20 2012

Keywords

Comments

This sequence agrees with A109043 for 0
For a guide to related sequences, see A204892.
Sequence agrees with A109043 at least up to 6400. - Michel Marcus, Mar 14 2018
If Polignac's conjecture is true, then this is a duplicate of A109043. - Robert Israel, Mar 14 2018

Examples

			1 = (5-3)/2=(7-3)/4=(13-3)/6=(11-3)/8=...
2 = (5-3)/1=(11-5)/3=(7-3)/5=(17-3)/7=...

Links

Crossrefs

Cf. A066043, A109043, A204900, A204892, A210530.

Programs

  • Mathematica
    (See the program at A204900.)
  • PARI
    a(n) = {forprime(p=5,,forprime(q=3, p-1, d = p-q; if ((d % n) == 0, return (d));););} \\ Michel Marcus, Mar 14 2018

A204907 Least k such that n divides A204906(k), the k-th difference of two primes >=5.

Original entry on oeis.org

1, 1, 2, 3, 8, 2, 11, 4, 16, 8, 23, 7, 29, 11, 38, 17, 47, 16, 56, 31, 67, 23, 80, 22, 108, 29, 92, 49, 140, 38, 121, 37, 137, 47, 194, 46, 172, 56, 191, 68, 212, 67, 234, 110, 233, 80, 255, 79, 277, 108
Offset: 1

Views

Author

Clark Kimberling, Jan 20 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Examples

			a(5)=8 because 5 divides 10, which is A204906(8).
(The 8th difference of primes>=5 is s(5)-s(2)=17-7=10.)

Crossrefs

Cf. A204908, A204900, A204892.

Programs

  • Mathematica
    (See the program at A204908.)

A204915 Least k such that n divides A204914(k), the k-th difference of two squared primes.

Original entry on oeis.org

1, 3, 2, 3, 1, 6, 2, 3, 4, 5, 11, 6, 7, 8, 4, 3, 22, 10, 16, 5, 2, 18, 43, 6, 29, 25, 37, 8, 46, 14, 37, 9, 11, 33, 17, 10, 89, 49, 7, 5, 79, 20, 67, 18, 4, 43, 118, 9, 92, 53, 22, 25, 135, 54, 11, 8, 16, 73, 137, 14
Offset: 1

Views

Author

Clark Kimberling, Jan 20 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A204908, A204900, A204892.

Programs

  • Mathematica
    (See the program at A204916.)

A204917 Least j such that n divides s(k)-s(j) for some k>j, where s(j)=(prime(j))^2.

Original entry on oeis.org

1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, 1, 2, 1, 3, 7, 3, 1, 4, 1, 2, 1, 4, 1, 3, 1, 5, 2, 4, 11, 4, 1, 2, 1, 5, 1, 3, 1, 7, 13, 3, 1, 8, 1, 4, 15, 9, 1, 2, 1, 7, 1, 4
Offset: 1

Views

Author

Clark Kimberling, Jan 20 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A204916, A204908, A204900, A204892.

Programs

  • Mathematica
    (See the program at A204916.)

A204918 Least prime p^2 such that n divides p^2-q^2 for some prime q satisfying q

Original entry on oeis.org

9, 25, 25, 25, 9, 49, 25, 25, 49, 49, 169, 49, 121, 121, 49, 25, 361, 121, 289, 49, 25, 289, 841, 49, 529, 361, 841, 121, 961, 169, 841, 121, 169, 529, 289, 121, 1849, 961, 121, 49, 1849, 289, 1681, 289, 49, 841, 2809, 121, 2209, 961, 361, 361, 3481
Offset: 1

Views

Author

Clark Kimberling, Jan 20 2012

Keywords

Comments

For a guide to related sequences, see A204892.

Crossrefs

Cf. A204916, A204908, A204900, A204892.

Programs

  • Mathematica
    (See the program at A204916.)
Previous Showing 11-20 of 22 results. Next

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