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.

Previous Showing 11-16 of 16 results.

A114263 Smallest number m such that prime(n) + 2*prime(n+m) is a prime.

Original entry on oeis.org

1, 1, 1, 1, 1, 4, 5, 3, 2, 2, 3, 1, 1, 4, 5, 1, 5, 4, 2, 2, 2, 2, 1, 3, 1, 1, 8, 4, 1, 1, 2, 3, 9, 2, 5, 2, 2, 9, 6, 1, 1, 1, 1, 2, 3, 4, 1, 4, 5, 8, 11, 1, 11, 4, 5, 1, 4, 1, 5, 8, 1, 1, 1, 1, 2, 5, 1, 5, 9, 2, 1, 10, 3, 4, 4, 5, 5, 6, 7, 4, 1, 1, 2, 4, 13, 6, 6, 6, 7, 9, 1, 3, 1, 7, 3, 9, 1, 3, 3, 6, 3, 8, 2
Offset: 2

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Examples

			n=2: prime(2)+2*prime(2+1)=3+2*5=13 is prime, so a(2)=1;
n=3: prime(3)+2*prime(3+1)=5+2*7=19 is prime, so a(2)=1;
...
n=7: prime(7)+2*prime(7+1)=17+2*19=55 is not prime
...
prime(7)+2*prime(7+4)=17+2*31=79 is prime, so a(7)=4;

Links

Crossrefs

Cf. A114227, A114230, A073703, A114235, A114262, A114228, A114231, A114233, A114236.
Cf. A010051, A000040.

Programs

  • Haskell
    a114263 n = head [m | m <- [1..n],
                      a010051 (a000040 n + 2 * a000040 (n + m)) == 1]
-- Reinhard Zumkeller, Oct 31 2013
  • Mathematica
    Table[p1 = Prime[n1]; n2 = 1; p2 = Prime[n1 + n2]; While[cp = p1 + 2* p2; ! PrimeQ[cp], n2++; p2 = Prime[n1 + n2]]; n2, {n1, 2, 201}]

Extensions

Edited definition to conform to OEIS style. - Reinhard Zumkeller, Oct 31 2013

A114265 Smallest prime p greater than prime(n) such that 2*prime(n) + p is a prime.

Original entry on oeis.org

3, 5, 7, 17, 19, 17, 19, 23, 37, 31, 41, 53, 67, 53, 73, 61, 61, 71, 89, 97, 83, 83, 97, 103, 113, 109, 107, 139, 113, 127, 167, 139, 157, 179, 151, 197, 173, 173, 223, 211, 199, 239, 211, 227, 199, 233, 239, 227, 229, 233, 277, 241, 251, 271, 283, 271, 271, 281
Offset: 1

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Comments

Note that p is next prime after prime(n) iff prime(n) is a term in A173971. - Zak Seidov, Feb 11 2015

Examples

			n=1: 2*prime[1]+3=2*2+3=7 is prime, so a(1)=3;
n=2: 2*prime[2]+5=2*3+5=11 is prime, so a(2)=5;
...
n=4: 2*prime[4]+3=2*7+3=17 is prime, so a(4)=17.

Links

Crossrefs

Cf. A114227, A114230, A073703, A114235, A114262.
Cf. A010051, A000040, A173971.

Programs

  • Haskell
    a114265 n = head [p | let (q:qs) = drop (n - 1) a000040_list, p <- qs,
                      a010051 (2 * q + p) == 1]
-- Reinhard Zumkeller, Oct 31 2013
  • Mathematica
    Table[p1 = Prime[n1]; n2 = 1; p2 = Prime[n1 + n2]; While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; p2 = Prime[n1 + n2]]; p2, {n1, 1, 200}]
  • PARI
    a(n)=forprime(p=prime(n)+1,,if(isprime(2*prime(n)+p),return(p)))
vector(100,n,a(n)) \\ Derek Orr, Feb 11 2015

Extensions

Edited definition to conform to OEIS style. - Reinhard Zumkeller, Oct 31 2013

A114237 n(k) is the minimum n that requires at least k to make 2*Prime[n]+Prime[n-k] a prime.

Original entry on oeis.org

3, 12, 9, 10, 8, 17, 97, 20, 57, 50, 30, 56, 207, 171, 210, 134, 303, 127, 121, 275, 376, 278, 299, 413, 432, 251, 746, 949, 389, 742, 725, 1790, 1375, 3605, 783, 1812, 895, 1257, 2079, 2962, 4799, 3456, 6356, 1701, 5255, 4669, 5011, 7164, 3012, 8361, 11210
Offset: 1

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Examples

			2*Prime[3]+Prime[3-1]=2*5+3=13 is prime, so n(1)=3;
2*Prime[4]+Prime[4-1]=2*7+5=19 is prime, not counted
...
2*Prime[8]+Prime[8-1]=2*19+17=55 is not prime
2*Prime[8]+Prime[8-2]=2*19+13=51 is not prime
2*Prime[8]+Prime[8-3]=2*19+11=49 is not prime
...
2*Prime[8]+Prime[8-5]=2*19+5=43 is prime, so n(5)=8;

Crossrefs

Cf. A114227, A114230, A073703, A114229, A114232, A114234, A114235, A114236.

Programs

  • Mathematica
    Do[n[k] = 0, {k, 1, 2000}]; ct = 0; nm = 0; n2 = 0; n1 = 3; p1 = 5; While[ct < 200, n2 = 1; p2 = Prime[n1 - n2]; \ While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; p2 = Prime[n1 - n2]]; If[n[n2] == 0, n[ n2] = n1; If[n2 > nm, nm = n2]; If[n2 <= 200, ct++ ]; Print[Table[n[k], {k, 1, nm}]]]; n1++; p1 = Prime[n1]]

A114266 a(n) is the minimal number m that makes 2*prime(n)+prime(n+m) a prime.

Original entry on oeis.org

1, 1, 1, 3, 3, 1, 1, 1, 3, 1, 2, 4, 6, 2, 6, 2, 1, 2, 5, 5, 2, 1, 2, 3, 5, 3, 1, 6, 1, 1, 8, 2, 4, 7, 1, 9, 3, 2, 9, 7, 5, 10, 4, 5, 1, 5, 5, 1, 1, 1, 8, 1, 1, 4, 6, 2, 1, 2, 12, 10, 1, 11, 8, 3, 11, 2, 2, 1, 4, 1, 7, 2, 3, 2, 11, 2, 3, 3, 3, 1, 1, 5, 2, 5, 1, 7, 3, 3, 4, 6, 4, 7, 4, 1, 9, 5, 3, 2, 4, 7, 2, 9, 2
Offset: 1

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Examples

			n=1: 2*prime(1)+prime(1+1)=2*2+3=7 is prime, so a(1)=1;
n=2: 2*prime(2)+prime(2+1)=2*3+5=11 is prime, so a(2)=1;
...
n=4: 2*prime(4)+prime(4+1)=2*7+11=25 is not prime
...
2*prime(4)+prime(4+3)=2*7+17=31 is prime, so a(4)=3.

Links

Crossrefs

Cf. A114227, A114230, A073703, A114235, A114262, A114228, A114231, A114233, A114236, A114263, A114265, A114267.
Cf. A000040, A010051.

Programs

  • Haskell
    a114266 n = head [m | m <- [1..],
                      a010051 (2 * a000040 n + a000040 (n + m)) == 1]
-- Reinhard Zumkeller, Oct 29 2013
  • Mathematica
    Table[p1 = Prime[n1]; n2 = 1; p2 = Prime[n1 + n2]; While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; p2 = Prime[n1 + n2]]; n2, {n1, 1, 200}]
mnm[n_]:=Module[{m=1,p=2Prime[n]},While[!PrimeQ[p+Prime[n+m]],m++];m]; Array[mnm,110] (* Harvey P. Dale, Aug 05 2017 *)

Extensions

Edited definition to conform to OEIS style. - N. J. A. Sloane, Jan 08 2011

A114264 n(k) is the minimum number that require at least k to make Prime[n]+2*Prime[n+k] a prime.

Original entry on oeis.org

2, 10, 9, 7, 8, 40, 80, 28, 34, 73, 52, 174, 86, 105, 127, 161, 326, 225, 356, 154, 245, 394, 362, 350, 279, 586, 846, 321, 929, 1822, 1683, 1208, 1091, 2025, 947, 2108, 1361, 3181, 372, 2774, 1898, 3785, 3676, 2194, 6447, 2919, 3590, 7092, 4955, 2474, 19409
Offset: 1

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Examples

			Prime[2]+2*Prime[2+1]=3+2*5=13 is prime, so n(1)=2;
Prime[3]+2*Prime[3+1]=5+2*7=19 is prime, not counted;
...
Prime[7]+2*Prime[7+4]=17+2*31=79 is prime, so n(4)=7;

Crossrefs

Cf. A114227, A114230, A073703, A114235, A114262, A114229, A114232, A114234, A114237, A114263.

Programs

  • Mathematica
    Do[n[k] = 0, {k, 1, 2000}]; ct = 0; nm = 0; n2 = 0; n1 = 2; p1 = 3; While[ct < 200, n2 = 1; p2 = Prime[n1 + n2]; While[cp = p1 + 2*p2; ! PrimeQ[cp], n2++; p2 = Prime[n1 + n2]]; If[n[n2] == 0, n[n2] = n1; If[n2 > nm, nm = n2]; If[n2 <= 200, ct++ ]; Print[Table[n[k], {k, 1, nm}]]]; n1++; p1 = Prime[n1]]

A114267 a(n) = smallest k such that A114266(k) = n.

Original entry on oeis.org

1, 11, 4, 12, 19, 13, 34, 31, 36, 42, 62, 59, 142, 158, 247, 173, 240, 273, 204, 417, 231, 669, 172, 348, 965, 1003, 115, 1369, 370, 1244, 1251, 1373, 983, 1109, 2489, 1028, 2583, 1506, 6506, 6773, 7762, 5525, 2463, 6534, 6451, 3587, 4944, 3119, 3178, 4880
Offset: 1

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Comments

Inverse sequence to A114266.

Crossrefs

Cf. A114227, A114230, A073703, A114235, A114262, A114265, A114229, A114232, A114234, A114237, A114264, A114266.

Programs

  • Mathematica
    Do[n[k] = 0, {k, 1, 2000}]; ct = 0; nm = 0; n2 = 0; n1 = 1; p1 = 2; While[ct < 200, n2 = 1; p2 = Prime[n1 + n2]; While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; p2 = Prime[n1 + n2]]; If[n[n2] == 0, n[ n2] = n1; If[n2 > nm, nm = n2]; If[n2 <= 200, ct++ ]; Print[Table[n[k], {k, 1, nm}]]]; n1++; p1 = Prime[n1]]

Extensions

I clarified the definition. - N. J. A. Sloane, Jan 08 2011
Previous Showing 11-16 of 16 results.

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

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