A114236 -id:A114236 - cp's OEIS frontend

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

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

Lei Zhou, Nov 20 2005

			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;

Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

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

Cf. A010051, A000040.

a114263 n = head [m | m <- [1..n],
                      a010051 (a000040 n + 2 * a000040 (n + m)) == 1]
-- Reinhard Zumkeller, Oct 31 2013

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}]

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

Lei Zhou, Nov 20 2005

nonn

			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;

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

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

Lei Zhou, Nov 20 2005

			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.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

Cf. A000040, A010051.

a114266 n = head [m | m <- [1..],
                      a010051 (2 * a000040 n + a000040 (n + m)) == 1]
-- Reinhard Zumkeller, Oct 29 2013

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 *)

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

cp's OEIS Frontend

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

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

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

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Author

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Examples

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Crossrefs

Programs

Haskell

Mathematica

Extensions