

A120627


Least positive k such that both prime(n)+k and prime(n)+2k are prime, or 0 if no such k exists.


6



0, 2, 6, 6, 6, 24, 6, 12, 18, 12, 6, 30, 6, 18, 6, 18, 12, 6, 6, 18, 54, 24, 24, 12, 6, 6, 24, 30, 42, 18, 12, 18, 30, 12, 24, 6, 36, 18, 6, 54, 84, 30, 36, 18, 30, 12, 30, 54, 6, 42, 18, 12, 36, 6, 6, 48, 12, 6, 30, 36, 24, 54, 30, 36, 18, 36, 18, 30, 6, 24, 48, 30, 6, 24, 30, 18, 30
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Note that 6 divides a(n) for n>2.  T. D. Noe, Aug 29 2006
Van der Corput's theorem: There are infinitely many positive integers n, k such that n, n+nk, n+2nk are all prime.  Jonathan Vos Post, Apr 17 2007


REFERENCES

A. G. van der Corput, Uber Summen von Primzahlen und Primzahlquadraten," Math. Ann., 116 (1939) 150.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000
Terence Tao, Simons Lecture I: Structure and randomness in Fourier analysis and number theory, April 2007.


EXAMPLE

a(3)=6 because prime(3)=5 and 5+6 and 5+12 are primes.


MATHEMATICA

f[n_] := Block[{p = Prime[n], k = 1}, If[n == 1, 0, While[ ! PrimeQ[p + 2k]  ! PrimeQ[p + 4k], k++ ]; 2k] ]; Table[f[n], {n, 80}] (*Chandler*)
Join[{0}, Table[p=Prime[n]; k=2; While[ !PrimeQ[p+k]  !PrimeQ[p+2k], k=k+2]; k, {n, 2, 100}]]  T. D. Noe, Aug 29 2006


PROG

(PARI) a(n)=if(n<2, 0, my(p=prime(n), k); while(!isprime(p+k++)!isprime(p+2*k), ); k) \\ Charles R Greathouse IV, Apr 24 2015


CROSSREFS

Cf. A000040.
Sequence in context: A071888 A117217 A161331 * A089879 A087651 A078579
Adjacent sequences: A120624 A120625 A120626 * A120628 A120629 A120630


KEYWORD

easy,nonn


AUTHOR

Giovanni Teofilatto, Aug 25 2006


EXTENSIONS

Edited and extended by Ray Chandler and T. D. Noe, Aug 28 2006


STATUS

approved



