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 1-10 of 16 results. Next

A097524 Duplicate of A073703.

Original entry on oeis.org

3, 5, 3, 3, 7, 3, 3, 3, 7, 3, 5, 5, 7, 3, 3, 3, 13, 5, 3, 7, 3, 5, 7, 3, 3, 31, 5, 13, 5, 3, 3, 7, 3, 3
Offset: 1

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Author

Keywords

A114235 Largest prime p < prime(n) such that 2*prime(n) + p is a prime.

Original entry on oeis.org

3, 5, 7, 11, 13, 5, 13, 13, 17, 29, 31, 41, 43, 43, 31, 59, 59, 37, 53, 71, 73, 79, 89, 79, 101, 103, 89, 67, 113, 127, 127, 131, 103, 137, 149, 137, 157, 163, 163, 179, 181, 191, 193, 179, 197, 197, 223, 173, 211, 223, 227, 241, 229, 193, 223, 269, 269, 277, 263
Offset: 3

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Examples

			n=3: 2*prime(3)+3=2*5+3=13 is prime, so a(3)=3;
n=4: 2*prime(4)+5=2*7+5=19 is prime, so a(4)=5;
...
n=8: 2*prime(8)+17=2*19+17=55 is not prime
2*prime(8)+13=2*19+13=51 is not prime
...
2*prime(8)+5=2*19+5=43 is prime, so a(8)=5;

Links

Crossrefs

Cf. A114227, A114230, A073703.
Cf. A000040, A010051.

Programs

  • Haskell
    a114235 n = head [p | let q = a000040 n,
                      p <- reverse $ takeWhile (< q) a000040_list,
                      a010051 (2 * q + p) == 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++; If[n2 >= n1, Print[n1]]; p2 = Prime[n1 - n2]]; p2, {n1, 3, 202}]

Extensions

Edited definition to conform to OEIS style. - Reinhard Zumkeller, Oct 29 2013

A114262 p is the smallest prime that is greater than prime(n) such that prime(n)+2*p is a prime.

Original entry on oeis.org

5, 7, 11, 13, 17, 31, 41, 37, 37, 41, 47, 43, 47, 67, 73, 61, 83, 83, 79, 83, 89, 97, 97, 107, 103, 107, 151, 137, 127, 131, 139, 151, 191, 157, 179, 167, 173, 223, 199, 181, 191, 193, 197, 211, 227, 233, 227, 241, 257, 277, 307, 251, 313, 277, 283, 271, 293, 281
Offset: 2

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Examples

			n=2: prime[2]=3; 3+2*5=13 is prime, so a(2)=5;
n=3: prime[3]=5; 5+2*7=19 is prime, so a(3)=7;
...
n=7: prime[7]=17; 17+2*19=55 is not prime
17+2*23=63 is not prime
...
17+2*31=79 is prime, so a(7)=31.

Links

Crossrefs

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

Programs

  • Haskell
    a114262 n = head [q | let (p:ps) = drop (n - 1) a000040_list,
                      q <- ps, a010051 (p + 2 * q) == 1]
-- Reinhard Zumkeller, Oct 29 2013
  • Mathematica
    Table[p1 = Prime[n1]; n2 = 1; p2 = Prime[n1 + n2]; While[cp = p1 + 2* p2; ! PrimeQ[cp], n2++; p2 = Prime[n1 + n2]]; p2, {n1, 2, 201}]

Extensions

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

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

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

A073704 Smallest prime p such that also p-prime(n)*2 is a prime.

Original entry on oeis.org

7, 11, 13, 17, 29, 29, 37, 41, 53, 61, 67, 79, 89, 89, 97, 109, 131, 127, 137, 149, 149, 163, 173, 181, 197, 233, 211, 227, 223, 229, 257, 269, 277, 281, 311, 307, 317, 331, 337, 349, 389, 367, 389, 389, 397, 401, 433, 449, 457, 461, 479, 491, 487, 509, 521
Offset: 1

Views

Author

Reinhard Zumkeller, Aug 04 2002

Keywords

Crossrefs

Cf. A073703, A001747, A000040, A020484.

A114234 n(k) is the minimum n that requires at least k to make 2*Prime[n]+Prime[k] a prime.

Original entry on oeis.org

3, 11, 5, 47, 17, 106, 64, 157, 133, 26, 236, 308, 72, 496, 122, 207, 152, 142, 197, 259, 514, 497, 1266, 1482, 2005, 2193, 1380, 964, 3662, 534, 4055, 667, 2513, 6083, 1794, 689, 3332, 5771, 3713, 4587, 3450, 12520, 5712, 3242, 10252, 18663, 11912, 25124
Offset: 2

Views

Author

Lei Zhou, Nov 20 2005

Keywords

Comments

Shows the first 204 items; The first appearance in A114233; Sequence is defined for all k>=2.

Examples

			k=2: 2*Prime[3]+Prime[2]=13 is prime, so n(2)=3;
2*Prime[4]+Prime[2]=17
2*Prime[5]+Prime[2]=25, ... 2*Prime[5]+Prime[4]=29 ==> n(4)=5;

Crossrefs

Cf. A073703, A114227, A114229, A114232, A114233.

Programs

  • Mathematica
    Do[n[k] = 0, {k, 2, 2000}]; ct = 0; nm = 0; n2 = 0; n1 = 3; p1 = 5; While[ct < 200, n2 = 1; p2 = Prime[n2]; While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; p2 = Prime[n2]]; If[n[n2] == 0, n[ n2] = n1; If[n2 > nm, nm = n2]; If[n2 <= 201, ct++ ]; Print[Table[n[k], {k, 2, nm}]]]; n1++; p1 = Prime[n1]];

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]]
Showing 1-10 of 16 results. Next

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