A073704 -id:A073704 - cp's OEIS frontend

A073703 Smallest prime p such that also p+prime(n)*2 is a prime.

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, 13, 5, 3, 5, 3, 3, 31, 5, 7, 3, 3, 3, 11, 3, 3, 3, 13, 13, 5, 7, 7, 31, 3, 5, 3, 7, 3, 7, 3, 19, 5, 7, 11, 3, 7, 3, 3, 43, 5, 5, 3, 3, 19, 3, 7, 3, 19, 11, 19, 11, 3, 43, 13, 5, 7, 3, 3, 13, 3

Offset: 1

Reinhard Zumkeller, Aug 04 2002

nonn

If Polignac's conjecture (1849) is correct, the sequence is defined for all n (as is A020483).

Also: least k-prime(n) such that k-prime(n) and k+prime(n) are both primes. - Pierre CAMI, Aug 27 2004

			n=5: prime(5)=11; 2+11*2=24, 3+11*2=25 and 5+11*2=27 are not prime, but 7+11*2=29 is prime, therefore a(5)=7.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A073704, A001747, A000040, A020483.

Cf. A010051.

a073703 n = head [p | p <- a000040_list, a010051 (p + 2 * a000040 n) == 1]
-- Reinhard Zumkeller, Oct 29 2013

f[n_] := Block[{k = Prime[n], p = Prime[n]}, While[ !PrimeQ[k - p] || !PrimeQ[k + p], k++ ]; k - p]; Table[ f[n], {n, 95}] (* Robert G. Wilson v, Aug 28 2004 *)

forprime(q=2,500,forprime(p=2,default(primelimit),if(isprime(2*q+p),print1(p", ");next(2)));error("Not enough precomputed primes")) \\ Charles R Greathouse IV, Aug 21 2011

Merged with Pierre CAMI's submission of Aug 2004 - R. J. Mathar, Jul 29 2008

A076812 a(n) = the smallest prime p such that p-prime(n)*4 is prime.

Original entry on oeis.org

11, 17, 23, 31, 47, 59, 71, 79, 97, 127, 127, 151, 167, 179, 191, 223, 239, 251, 271, 307, 311, 347, 337, 359, 401, 409, 419, 431, 439, 457, 521, 541, 571, 563, 599, 607, 631, 659, 673, 709, 719, 727, 769, 809, 811, 809, 857, 911, 911, 919, 937, 967, 967

Offset: 1

Cino Hilliard, Nov 19 2002

Hans Rademacher, Lectures on Elementary Number Theory, 1964: Primes in an arithmetic progression - Proof of Dirichlet's Theorem. pp. 121-136.

Cf. A000040, A073703, A073704.

Edited by Don Reble, May 03 2006

A190664 Least semiprime whose prime factors differ by 2*prime(n).

Original entry on oeis.org

21, 55, 39, 51, 203, 87, 111, 123, 371, 183, 335, 395, 623, 267, 291, 327, 1703, 635, 411, 1043, 447, 815, 1211, 543, 591, 7223, 1055, 2951, 1115, 687, 771, 1883, 831, 843, 4043, 1535, 951, 1655, 1011, 1047, 12059, 1835, 2723, 1167, 1191, 1203, 4763, 1347

Offset: 1

Michel Lagneau, May 16 2011

nonn

			a(5) = 203 because 203 = 7*29, and 29 - 7 = 22 = 2*11 = 2*prime(5).

Cf. A073703, A073704.

f[n_] := Block[{p=3}, While[! PrimeQ[p+2*Prime[n]], p=NextPrime[p]]; p*(p+2*Prime[n])]; Table[f[n], {n, 1, 60}]

a(n) = A073703(n) * A073704(n).

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A073703 Smallest prime p such that also p+prime(n)*2 is a prime.

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A076812 a(n) = the smallest prime p such that p-prime(n)*4 is prime.

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A190664 Least semiprime whose prime factors differ by 2*prime(n).

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