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 1-6 of 6 results.

A057473 Let prime(i) = i-th prime, let twin(n) = (P,Q) be n-th pair of twin primes; sequence gives prime(Q).

Original entry on oeis.org

11, 17, 41, 67, 127, 191, 283, 367, 563, 599, 797, 877, 1087, 1171, 1217, 1447, 1523, 1741, 1847, 2081, 2351, 2909, 3019, 3299, 3761, 4153, 4421, 4567, 4787, 4943, 6229, 6323, 6361, 6661, 6863, 8117, 8233, 8389, 8527, 8761, 9319, 10009, 10457, 10589
Offset: 1

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Author

James Sellers, Sep 11 2000

Keywords

Examples

			The 3rd pair of twin primes is twin(3) = (11,13), so a(3) = prime(13) = 41.

Links

Crossrefs

Cf. A006512, A057470, A151800.

Programs

  • Mathematica
    Prime[#]&/@Transpose[Select[Partition[Prime[Range[300]],2,1], Last[#]- First[#] == 2&]][[2]] (* Harvey P. Dale, Nov 29 2011 *)

Formula

From Amiram Eldar, Feb 14 2025: (Start)
a(n) = prime(A006512(n)).
a(n) = A151800(A151800(A057470(n))). (End)

A096474 Difference prime(q+2) - prime(q) as q runs through the lesser members of twin primes (A001359).

Original entry on oeis.org

6, 6, 10, 8, 18, 12, 6, 14, 16, 12, 24, 18, 24, 18, 16, 14, 24, 18, 24, 18, 10, 12, 18, 40, 28, 20, 24, 18, 28, 10, 12, 12, 8, 8, 22, 16, 12, 12, 14, 14, 26, 36, 24, 30, 24, 8, 18, 30, 12, 22, 22, 16, 18, 24, 10, 14, 18, 14, 10, 20, 10, 32, 32, 12, 10, 44, 30, 18, 16, 36, 14, 12
Offset: 1

Views

Author

Labos Elemer, Jun 23 2004

Keywords

Examples

			{q, q+2} = {17, 19} is the 4th twin-pair and prime(19) - prime(17) = 67 - 59 = 8, so a(4) = 8.

Links

Crossrefs

Cf. A001359, A006512, A057470, A057473.

Programs

  • Mathematica
    {ta=Table[0, {1300}], tb=Table[0, {1300}], tc=Table[0, {1300}], u=1}; Do[s=Prime[n+1]-Prime[n];If[Equal[s, 2], ta[[u]]=Prime[Prime[n+1]]-Prime[Prime[n]];tb[[u]]=n; tc[[u]]=Prime[n];u=u+1], {n, 1, 10000}];ta
Prime[#[[2]]]-Prime[#[[1]]]&/@Select[Partition[Prime[Range[500]],2,1],#[[2]]-#[[1]]==2&] (* Harvey P. Dale, Dec 26 2023 *)
  • PARI
    lista(nn) = {forprime(q=2, nn, if (isprime(q+2), print1(prime(q+2)-prime(q), ", ")););} \\ Michel Marcus, Jul 27 2017

Formula

a(n) = prime(A006512(n)) - prime(A001359(n)).
a(n) = A057473(n) - A057470(n). - Michel Marcus, Jul 27 2017

A080698 Product of twin-prime-indexed primes and their lower bound twin prime.

Original entry on oeis.org

15, 55, 341, 1003, 3161, 7339, 16343, 25063, 55247, 62809, 105901, 127991, 190277, 220223, 236597, 325291, 358261, 463487, 512263, 641593, 812327, 1213843, 1293431, 1502399, 1944893, 2351677, 2633803, 2806733, 3050519, 3250847
Offset: 1

Views

Author

Cino Hilliard, Mar 04 2003

Keywords

Examples

			The 3rd pair of twin primes is twin(3) = (11,13), prime(11) = 31. a(3) = 31*11 = 341.

Links

Crossrefs

Cf. A057470.

Programs

  • Mathematica
    # Prime[#]&/@Select[Partition[Prime[Range[200]],2,1],#[[2]]-#[[1]]==2&][[All,1]] (* Harvey P. Dale, Apr 10 2019 *)
  • PARI
    twipxpindex(n) = {sr=0; pr=1; for(x=1,n, p1=prime(x); p2=prime(x+1); if((p2-p1)==2, pr=p1*prime(prime(x)); sr+=1.0/pr; print1(pr" ")); ); print(); print(sr) }

Formula

Let prime(i) = i-th prime, let twin(n) = (P, Q) be n-th pair of twin primes; sequence gives prime(P)*P.

A080699 Product of twin-prime-indexed primes and their upper bound twin prime.

Original entry on oeis.org

25, 77, 403, 1121, 3379, 7697, 16897, 25769, 56341, 63983, 107447, 129709, 192403, 222529, 238999, 328157, 361259, 466933, 515909, 645719, 817009, 1219637, 1299433, 1508917, 1952359, 2359943, 2642597, 2815831, 3060037, 3260713
Offset: 1

Views

Author

Cino Hilliard, Mar 04 2003

Keywords

Examples

			The 3rd pair of twin primes is twin(3) = (11,13), prime(11) = 31, a(3) = 31*13 = 403.

Crossrefs

Cf. A057470.

Programs

  • PARI
    twipxpindex2(n) = {sr=0; pr=1; for(x=1,n, p1=prime(x); p2=prime(x+1); if((p2-p1)==2, pr=p2*prime(prime(x)); sr+=1.0/pr; print1(pr" ")); ); print(); print(sr) }

Formula

Let prime(i) = i-th prime, let twin(n) = (P, Q) be n-th pair of twin primes; sequence gives prime(P)*Q.

A080700 Product of upper bound twin-prime-indexed primes and their lower bound twin prime.

Original entry on oeis.org

33, 85, 451, 1139, 3683, 7831, 16697, 26057, 56863, 64093, 109189, 130673, 194573, 223661, 239749, 328469, 363997, 468329, 519007, 647191, 815797, 1218871, 1301189, 1520839, 1959481, 2363057, 2648179, 2817839, 3068467, 3257437
Offset: 1

Views

Author

Cino Hilliard, Mar 04 2003

Keywords

Examples

			The 3rd pair of twin primes is twin(3) = (11,13), prime(13) = 41, a(3) = 41*11 = 451.

Crossrefs

Cf. A057470, A057473.

Programs

  • Mathematica
    Prime[Last[#]]First[#]&/@Select[Partition[Prime[Range[200]],2,1], Last[#]- First[#] ==2&]  (* Harvey P. Dale, Apr 23 2011 *)
  • PARI
    twipxpindex3(n) = {sr=0; pr=1; for(x=1,n, p1=prime(x); p2=prime(x+1); if((p2-p1)==2, pr=p1*prime(prime(x+1)); sr+=1.0/pr; print1(pr" ")); ); print(); print(sr) }

Formula

Let prime(i) = i-th prime, let twin(n) = (P, Q) be n-th pair of twin primes; sequence gives prime(Q)*P.

A080701 Product of upper bound twin-prime-indexed primes and their upper bound twin prime.

Original entry on oeis.org

55, 119, 533, 1273, 3937, 8213, 17263, 26791, 57989, 65291, 110783, 132427, 196747, 226003, 242183, 331363, 367043, 471811, 522701, 651353, 820499, 1224689, 1307227, 1527437, 1967003, 2371363, 2657021, 2826973, 3078041, 3267323
Offset: 1

Views

Author

Cino Hilliard, Mar 04 2003

Keywords

Examples

			The 3rd pair of twin primes is twin(3) = (11,13), prime(13) = 41, a(3) = 41*13 = 533.

Crossrefs

Cf. A057470, A057473.

Programs

  • Mathematica
    #*Prime[#]&/@(Transpose[Select[Partition[Prime[Range[200]],2,1], Last[#]- First[#] ==2&]][[2]]) (* Harvey P. Dale, Jun 04 2014 *)

Formula

Let prime(i) = i-th prime, let twin(n) = (P, Q) be n-th pair of twin primes; sequence gives prime(Q)*Q.
Showing 1-6 of 6 results.

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