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 1-5 of 5 results.

A098420 Members of prime triples (p,q,r) with p < q < r = p + 6.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 23, 37, 41, 43, 47, 67, 71, 73, 97, 101, 103, 107, 109, 113, 191, 193, 197, 199, 223, 227, 229, 233, 277, 281, 283, 307, 311, 313, 317, 347, 349, 353, 457, 461, 463, 467, 613, 617, 619, 641, 643, 647, 821, 823, 827, 829, 853, 857, 859, 863
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 07 2004

Keywords

Comments

A098418(a(n)) > 0; complement of A098419 in A000040.
Union of A007529, A098414 and A098415.

Links

Crossrefs

Cf. A000040, A007529, A098414, A098415, A098418, A098419.

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[p2=p+2]&&PrimeQ[p6=p+6], AppendTo[lst, p];AppendTo[lst, p2];AppendTo[lst, p6]];If[PrimeQ[p4=p+4]&&PrimeQ[p6=p+6], AppendTo[lst, p];AppendTo[lst, p4];AppendTo[lst, p6]], {n, 6!}];Union[lst] (* Vladimir Joseph Stephan Orlovsky, Sep 25 2008 *)

A098418 Number of prime triples (p,q,r) with p

Original entry on oeis.org

0, 0, 1, 2, 3, 3, 3, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 07 2004

Keywords

Comments

0 <= a(n) <= 3;
a(A098419(n))=0; a(A098420(n))>0; a(A098421(n))=1; a(A098422(n))=2; a(A098423(n))=3.

Examples

			A000040(13)=41: A007529(7)=41, A098414(6)=41 and
A098415(k)<>41 for all k, therefore a(13)=2.

Links

Crossrefs

Cf. A007529, A098414, A098415.

A098421 Primes occurring in exactly one prime triple (p,q,r) with p

Original entry on oeis.org

5, 23, 37, 47, 67, 71, 73, 97, 113, 191, 199, 223, 233, 277, 281, 283, 307, 317, 347, 349, 353, 457, 467, 613, 617, 619, 641, 643, 647, 821, 829, 853, 863, 877, 887, 1087, 1097, 1277, 1279, 1283, 1297, 1307, 1423, 1433, 1447, 1451, 1453, 1481, 1493, 1607, 1609
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 07 2004

Keywords

Comments

A098418(a(n)) = 1; subsequence of A098420.

Links

Crossrefs

Cf. A098419, A098422, A098423.

A098422 Primes occurring in exactly two prime triples (p,q,r) with p

Original entry on oeis.org

7, 19, 41, 43, 101, 109, 193, 197, 227, 229, 311, 313, 461, 463, 823, 827, 857, 859, 881, 883, 1091, 1093, 1301, 1303, 1427, 1429, 1483, 1489, 1871, 1877, 1997, 1999, 2083, 2087, 2687, 2689, 3253, 3257, 3461, 3467, 4517, 4519, 4787, 4789, 5231, 5233, 5651
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 07 2004

Keywords

Comments

A098418(a(n)) = 2; subsequence of A098420.

Links

Crossrefs

Cf. A098419, A098421, A098423.

Programs

  • Mathematica
    Select[Tally[Flatten[Select[Partition[Prime[Range[800]],3,1],#[[3]]- #[[1]] == 6&]]],#[[2]]==2&][[All,1]] (* Harvey P. Dale, Jun 01 2019 *)

A098423 Primes occurring in exactly three prime triples (p,q,r) with p

Original entry on oeis.org

11, 13, 17, 103, 107, 1487, 1873, 3463, 5653, 15733, 16063, 16067, 19423, 19427, 21017, 22277, 43783, 43787, 55337, 79693, 88813, 101113, 144167, 165707, 166847, 195737, 201827, 225347, 247607, 257863, 266683, 268817, 276043, 284743
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 07 2004

Keywords

Comments

A098418(a(n)) = 3; subsequence of A098420.
This sequence consists of all integers of the form (prime(m)*prime(m+4)+36)/prime(m+2), for m>0, where prime(m) = A000040(m). Also note that the integers resulting from that rule equal prime(m+2), therefore a(n) also consists of all integers of the form sqrt[prime(m)*prime(m+4)+36]. - Richard R. Forberg, Jan 11 2016

Examples

			A000040(27)=103: A007529(11)=103, A098414(10)=103 and A098415(9)=103, therefore 103 is a term.

Links

Crossrefs

Cf. A098419, A098421, A098422.
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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