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 10 results.

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;
		

Crossrefs

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.
		

Crossrefs

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

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

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;
		

Crossrefs

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;
		

Crossrefs

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.
		

Crossrefs

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

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.
		

Crossrefs

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

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

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
Showing 1-10 of 10 results.