A114262 -id:A114262 - cp's OEIS frontend

A175914 Primes p such that p+2*q is prime, where q is the prime after p.

3, 5, 7, 11, 13, 41, 43, 59, 89, 101, 103, 113, 127, 179, 181, 191, 193, 223, 241, 269, 277, 293, 307, 311, 313, 337, 359, 421, 431, 479, 491, 521, 599, 613, 631, 673, 773, 787, 821, 823, 863, 881, 883, 907, 911, 919, 929, 937, 953, 967, 1019, 1021, 1039, 1061, 1109, 1151, 1171

Offset: 1

Zak Seidov, Dec 05 2010

nonn

A174915 gives lesser of twin primes in this sequence.

Values of p+2*q are in A094105. [Zak Seidov, Sep 07 2012]

			3 and 5 are consecutive primes, and 3+2*5 = 13 is prime. Hence 3 is in the sequence.
59 and 61 are consecutive primes, and 59+2*61 = 181 is prime. Hence 59 is in the sequence.

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A094105, A114262, A174915, A001359.

[p: p in PrimesUpTo(1200) | IsPrime(p+2*NextPrime(p))]; // Klaus Brockhaus, Dec 06 2010

p = 3; Reap[Do[q = NextPrime[p]; If[PrimeQ[p + 2 q], Sow[p]]; p = q, {10^3}]][[2, 1]] (* Zak Seidov, Oct 14 2012 *)

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

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

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

Lei Zhou, Nov 20 2005

Note that p is next prime after prime(n) iff prime(n) is a term in A173971. - Zak Seidov, Feb 11 2015

			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.

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

Cf. A114227, A114230, A073703, A114235, A114262.

Cf. A010051, A000040, A173971.

a114265 n = head [p | let (q:qs) = drop (n - 1) a000040_list, p <- qs,
                      a010051 (2 * q + p) == 1]
-- Reinhard Zumkeller, Oct 31 2013

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}]

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

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

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

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

Lei Zhou, Nov 20 2005

nonn

			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;

Cf. A114227, A114230, A073703, A114235, A114262, A114229, A114232, A114234, A114237, A114263.

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

Lei Zhou, Nov 20 2005

nonn

Inverse sequence to A114266.

Cf. A114227, A114230, A073703, A114235, A114262, A114265, A114229, A114232, A114234, A114237, A114264, A114266.

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]]

I clarified the definition. - N. J. A. Sloane, Jan 08 2011

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A175914 Primes p such that p+2*q is prime, where q is the prime after p.

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

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A114265 Smallest prime p greater than prime(n) such that 2*prime(n) + p is 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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A114264 n(k) is the minimum number that require at least k to make Prime[n]+2*Prime[n+k] a prime.

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A114267 a(n) = smallest k such that A114266(k) = n.

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