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

A114230 Largest prime p < prime(n) such that prime(n) + 2 * p is a prime.

Original entry on oeis.org

2, 3, 5, 3, 5, 13, 17, 19, 19, 29, 23, 31, 29, 31, 43, 19, 59, 53, 61, 59, 59, 79, 67, 83, 61, 89, 103, 101, 109, 113, 109, 97, 131, 109, 149, 137, 149, 127, 163, 139, 149, 109, 149, 163, 197, 191, 197, 223, 227, 229, 211, 239, 241, 241, 223, 241, 269, 233, 271, 269
Offset: 2

Views

Author

Lei Zhou, Nov 18 2005

Keywords

Examples

			prime(2)=3, 3+2*2=7 is prime, so a(2)=2;
prime(3)=5, 5+2*3=11 is prime, so a(3)=3;
...
prime(11)=31, 31+2*29=89 is prime, so a(11)=29.

Links

Crossrefs

Cf. A114227.
Cf. A000040, A010051.

Programs

  • Haskell
    a114230 n = head [p | let q = a000040 n,
                      p <- reverse $ takeWhile (< q) a000040_list,
                      a010051 (q + 2 * p) == 1]
-- Reinhard Zumkeller, Oct 29 2013
  • Mathematica
    Table[p1 = Prime[n1]; n2 = n1 - 1; p2 = Prime[n2]; While[cp = p1 + 2*p2; ! PrimeQ[cp], n2--; If[n2 == 0, Print[n1]]; p2 = Prime[n2]]; p2, {n1, 2, 201}]
lp[n_]:=Module[{p=NextPrime[n,-1]},While[!PrimeQ[n+2p],p=NextPrime[p,-1]];p]; Table[lp[p],{p,Prime[Range[2,70]]}] (* Harvey P. Dale, Jan 17 2022 *)

Extensions

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

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

A114228 Smallest number m such that prime(n)+2*prime(m) is a prime.

Original entry on oeis.org

1, 2, 1, 2, 1, 2, 1, 2, 4, 2, 1, 2, 1, 2, 2, 4, 2, 1, 6, 2, 1, 2, 4, 1, 2, 1, 2, 1, 4, 1, 2, 4, 3, 4, 2, 2, 1, 2, 2, 4, 3, 2, 1, 4, 7, 5, 1, 2, 1, 2, 8, 3, 2, 2, 2, 4, 2, 1, 6, 3, 4, 1, 2, 1, 4, 2, 3, 2, 1, 2, 4, 2, 2, 1, 2, 12, 1, 8, 3, 4, 3, 6, 2, 1, 2, 4, 1, 2, 1, 12, 11, 1, 14, 1, 2, 4, 6, 7, 2, 3, 2, 2, 8
Offset: 2

Views

Author

Lei Zhou, Nov 18 2005

Keywords

Comments

a(A114229(n)) = n for n >=1 and a(m) <> n for m < A114229(n). - Reinhard Zumkeller, Oct 31 2013

Examples

			prime(2)=3, 3+2*prime(1)=7 is prime, so a(2)=1;
prime(3)=5, 5+2*prime(2)=11 is prime, so a(3)=2;
...
prime(20)=71, 71+2*prime(6)=97 is prime, so a(20)=6.

Links

Crossrefs

Cf. A114227.
Cf. A010051, A000040.

Programs

  • Haskell
    a114228 n = head [m | m <- [1..],
                      a010051 (a000040 n + 2 * a000040 m) == 1]
-- Reinhard Zumkeller, Oct 31 2013
  • Mathematica
    Table[p1 = Prime[n1]; n2 = 1; p2 = 2; While[ cp = p1 + 2*p2; ! PrimeQ[cp], n2++; p2 = Prime[n2]]; n2, {n1, 2, 201}]

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

A114229 Smallest number m such that A114228(m) = n.

Original entry on oeis.org

2, 3, 34, 10, 47, 20, 46, 52, 221, 462, 92, 77, 619, 94, 319, 2176, 263, 154, 700, 1980, 1336, 928, 2477, 3243, 428, 461, 2146, 4224, 1456, 2735, 3373, 5319, 6439, 4522, 4508, 4516, 11073, 1814, 9940, 10746, 17523, 6680, 16409, 10023, 16107, 14289
Offset: 1

Views

Author

Lei Zhou, Nov 18 2005

Keywords

Comments

Sequence is defined for all n>=1.
A114228(a(n)) = n and A114228(m) <> n for m < a(n).

Crossrefs

Cf. A114228, A114227.

Programs

  • Haskell
    import Data.List (elemIndex); import Data.Maybe (fromJust)
a114229 = (+ 2) . fromJust . (`elemIndex` (map a114228 [2..]))
-- Reinhard Zumkeller, Oct 31 2013
  • Mathematica
    Do[ns[k] = 0, {k, 1, 2000}]; n2 = 0; n1 = 1; While[n2 <= 200, n1++; p1 = Prime[n1]; n2 = 1; p2 = 2; While[cp = p1 + 2*p2; ! PrimeQ[cp], n2++; p2 = Prime[n2]]; If[ns[n2] == 0, ns[n2] = n1; Print[n2, "[", n1, "]"]]]; Table[ns[k], {k, 1, n2}]

Extensions

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

A114231 Smallest number m such that prime(n) + 2*prime(n-m) is a prime.

Original entry on oeis.org

1, 1, 1, 3, 3, 1, 1, 1, 2, 1, 3, 2, 4, 4, 2, 9, 1, 3, 2, 4, 5, 1, 5, 2, 8, 3, 1, 3, 1, 1, 3, 8, 2, 6, 1, 4, 3, 8, 2, 7, 7, 14, 9, 7, 1, 4, 3, 1, 1, 1, 5, 1, 1, 2, 8, 4, 1, 8, 2, 4, 1, 8, 3, 9, 5, 3, 2, 1, 4, 1, 4, 4, 2, 3, 2, 4, 2, 12, 3, 1, 1, 3, 12, 2, 1, 2, 5, 5, 3, 3, 10, 4, 19, 1, 6, 4, 8, 7, 2, 5, 9, 2, 3
Offset: 2

Views

Author

Lei Zhou, Nov 18 2005

Keywords

Examples

			n=2, prime(2)+2*prime(2-1)=3+2*2=7 is prime, so a(2)=1;
n=3, prime(3)+2*prime(3-1)=5+2*3=11 is prime, so a(3)=1;
...
n=17, prime(17)+2*prime(17-9)=59+2*19=97 is prime, so a(17)=9.

Links

Crossrefs

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

Programs

  • Haskell
    a114231 n = head [m | m <- [1..],
                      a010051 (a000040 n + 2 * a000040 (n - m)) == 1]
-- Reinhard Zumkeller, Oct 31 2013
  • Mathematica
    Table[p1 = Prime[n1]; n2 = n1 - 1; p2 = Prime[n2]; While[cp = p1 + 2*p2; ! PrimeQ[cp], n2--; If[n2 == 0, Print[n1]]; p2 = Prime[n2]]; n1 - n2, {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

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

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]];
Showing 1-10 of 16 results. Next

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