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.

A114233 Smallest number m such that 2*prime(n) + prime(m) is a prime.

Original entry on oeis.org

2, 2, 4, 2, 2, 2, 4, 2, 3, 3, 4, 2, 2, 2, 6, 3, 2, 4, 2, 3, 4, 2, 2, 11, 3, 6, 3, 2, 2, 4, 2, 2, 6, 3, 2, 3, 2, 2, 11, 3, 4, 2, 2, 2, 5, 2, 2, 2, 6, 6, 3, 4, 4, 11, 2, 3, 2, 4, 2, 4, 2, 8, 3, 4, 5, 2, 4, 2, 2, 14, 3, 3, 2, 2, 8, 2, 4, 2, 8, 5, 8, 5, 2, 14, 6, 3, 4, 2, 2, 6, 2, 11, 5, 2, 2, 4, 2, 3, 2, 2, 2, 6, 5
Offset: 3

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Examples

			n=3: 2*prime(3)+prime(2)=2*5+3=13 is prime, so a(3)=2;
n=4: 2*prime(4)+prime(2)=2*7+3=17 is prime, so a(4)=2;
n=5: 2*prime(5)+prime(2)=2*11+3=25 is not prime
...
2*prime(5)+prime(4)=2*11+7=29 is prime, so a(5)=4.

Links

Crossrefs

Cf. A073703, A114227, A114228, A114231.
Cf. A010051, A000040.

Programs

  • Haskell
    a114233 n = head [m | m <- [1 .. n],
                      a010051' (2 * a000040 n + a000040 m) == 1]
-- Reinhard Zumkeller, Oct 31 2013
  • Mathematica
    Table[p1 = Prime[n1]; n2 = 1; p2 = Prime[n2]; While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; If[n2 >= n1, Print[n1]]; p2 = Prime[n2]]; n2, { n1, 3, 202}]
snm[n_]:=Module[{m=1,p=2Prime[n]},While[!PrimeQ[p+Prime[m]],m++];m]; Array[ snm,110,3] (* Harvey P. Dale, Sep 30 2017 *)

Extensions

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

A114232 n(k) is the minimum number of n that need at least another number of k to make Prime[n]+2*Prime[n-k]a prime.

Original entry on oeis.org

2, 10, 5, 14, 22, 35, 41, 26, 17, 92, 170, 79, 190, 43, 164, 240, 175, 590, 94, 236, 446, 1004, 279, 920, 409, 971, 646, 1088, 502, 449, 1219, 1263, 2049, 1541, 2191, 915, 3727, 1886, 1394, 4506, 5014, 1524, 1181, 6323, 888, 3995, 4033, 6625, 9664, 13733
Offset: 1

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Comments

Shows the first 204 items; Sequenced defined for all k>=1; Sequence the first appearance of k in A114231

Examples

			k=1: Prime[2]+2*Prime[2-1]=3+2*2=7 is prime, so n(1)=2;
k=2: Prime[10]+2*Prime[10-2]=29+2*19=67 is prime, so n(2)=10;
while
Prime[3]+2*Prime[3-1]=5+2*3=11 is prime, not count according to the definition

Crossrefs

Cf. A114227, A114230, A114231.

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]];

A114236 Smallest number m such that 2*prime(n)+prime(n-m) is a prime.

Original entry on oeis.org

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

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Examples

			n=3: 2*prime(3)+prime(3-1)=2*5+3=13 is prime, so a(3)=1;
n=4: 2*prime(4)+prime(4-1)=2*7+5=19 is prime, so a(4)=1;
...
n=8: 2*prime(8)+prime(8-5)=2*19+5=43 is prime, so a(8)=5;

Links

Crossrefs

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

Programs

  • Haskell
    a114236 n = head [m | m <- [1..],
                      a010051 (2 * a000040 n + a000040 (n - m)) == 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++; If[n2 >= n1, Print[n1]]; p2 = Prime[n1 - n2]]; n2, {n1, 3, 202}]

Extensions

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

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

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
Showing 1-5 of 5 results.

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

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