

A256284


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


1



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
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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 53 and 5+6 are prime.
a(5)=4 because p=prime(5)=11, and d cannot be 2 because 112 is not prime (and 11+4 is composite as well) while for d=4, both 114 and 11+8 are prime.
a(7)=6 because p=17, d cannot be 2 because both 172 and 17+4 are composite, d cannot be 4 because though 174 is prime but 17+8 is composite, finally d is 6 because both 176 and 17+12 are prime.


MATHEMATICA

s={3}; Do[p=Prime[k]; Do[If[PrimeQ[pd]&&PrimeQ[p+2*d], s={s, d}; Break[]], {d, 2, p3, 2}], {k, 4, 200}]; s=Flatten[s]


PROG

(PARI) a(n, p=prime(n))=my(q=p); while(q=precprime(q1), if(isprime(3*p2*q), return(pq))); 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



