login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A283145
a(1)=5; for n > 1, and a(n) is the least prime p > a(n-1) such that both q = p + 2n and r = q + 2n + 2 are prime.
3
5, 7, 17, 23, 31, 41, 53, 67, 71, 89, 127, 149, 173, 199, 251, 281, 283, 347, 383, 409, 461, 479, 523, 593, 641, 691, 719, 773, 823, 887, 971, 1033, 1097, 1163, 1231, 1301, 1373, 1447, 1619, 1709, 1741, 1823, 1907
OFFSET
1,1
COMMENTS
Note that p,q,r are not required to be consecutive primes.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1)=5 because both 5 + 2 = 7 and 7 + 4 = 11 are prime;
n=2: d=4, p=7 because both p + d = 11 and 11 + 6 = 17 are prime;
n=3: d=6: primes 11,13 are not qualified while 17 + 6 = 23 and 23 + 8 = 31 are prime hence a(3)=17.
MATHEMATICA
m=0; p=3; s={}; Do[p = NextPrime[p]; m=m+2; While[!PrimeQ[p+m]||!PrimeQ[p+2*m+2], p=NextPrime[p]]; AppendTo[s, p], {50}]; s
PROG
(PARI) first(n)=my(v=vector(n), k=4); v[1]=5; forprime(p=5, , if(isprime(p+k) && isprime(p+2*k+2), v[k/2]=p; if(k==2*n, return(v)); k+=2)) \\ Charles R Greathouse IV, Mar 01 2017
CROSSREFS
Cf. A283159.
Sequence in context: A044966 A359297 A283159 * A191145 A145354 A214345
KEYWORD
nonn
AUTHOR
Zak Seidov, Mar 01 2017
EXTENSIONS
a(16)-a(17) corrected by Charles R Greathouse IV, Mar 01 2017
STATUS
approved