A256284 Smallest d > 0 such that both prime(n) - d and prime(n) + 2d are prime.

1, 3, 2, 4, 2, 6, 2, 4, 6, 8, 8, 10, 2, 6, 10, 6, 14, 6, 4, 12, 12, 10, 6, 8, 4, 2, 10, 2, 12, 18, 4, 6, 12, 12, 14, 8, 14, 16, 10, 6, 8, 10, 2, 16, 6, 14, 24, 28, 2, 4, 6, 8, 10, 6, 22, 6, 20, 8, 18, 12, 10, 26, 18, 2, 10, 14, 6, 10, 2, 22, 10, 8, 14, 20, 24, 6, 18, 4, 12, 10, 20, 30, 12, 20, 10, 6, 26

Offset

2,2

Comments

Apparently a(n) exists for any n > 1.

Smallest primes p with corresponding values of even d are {p,d}: {7,2}, {11,4}, {17,6}, {31,8}, {41,10}, {73,12}, {61,14}, {167,16}, {127,18}, {271,20}, {263,22}, {223,24}, {307,26}, {227,28}, {431,30}, {919,32}, {941,34}, {857,36}, {877,38}.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 2..10000

Example

a(3)=3 because p=prime(3)=5 and both 5-3 and 5+6 are prime.
a(5)=4 because p=prime(5)=11, and d cannot be 2 because 11-2 is not prime (and 11+4 is composite as well) while for d=4, both 11-4 and 11+8 are prime.
a(7)=6 because p=17, d cannot be 2 because both 17-2 and 17+4 are composite, d cannot be 4 because though 17-4 is prime but 17+8 is composite, finally d is 6 because both 17-6 and 17+12 are prime.

Mathematica

s={3}; Do[p=Prime[k]; Do[If[PrimeQ[p-d]&&PrimeQ[p+2*d], s={s, d}; Break[]], {d, 2, p-3, 2}], {k, 4, 200}]; s=Flatten[s]

Prog

(PARI) a(n, p=prime(n))=my(q=p); while(q=precprime(q-1), if(isprime(3*p-2*q), return(p-q))); -1 \\ Charles R Greathouse IV, Jun 04 2015

Crossrefs

Sequence in context: A099871 A157220 A304182 * A322979 A106288 A013633

Adjacent sequences: A256281 A256282 A256283 * A256285 A256286 A256287

Keyword

nonn

Author

Zak Seidov, Jun 03 2015

Status

approved