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”).
%I #38 Mar 11 2016 06:22:02
%S 3,7,13,19,43,103,109,193,229,313,349,401,463,491,509,643,743,761,823,
%T 859,883,911,997,1093,1237,1279,1303,1429,1459,1483,1489,1499,1571,
%U 1609,1637,1831,1873,1999,2003,2069,2083,2221,2239,2243,2251,2269,2273,2399
%N Primes prime(k) of the form (2*prime(k-1) + prime(k+1))/3.
%C Primes prime(k) such that A062234(k) = A062234(k-1). - _Thomas Ordowski_, Jan 03 2016
%C Primes prime(k) such that A001223(k) = 2*A001223(k-1). - _Robert Israel_, Jan 03 2016
%C Or, primes which are at 1/3 of the distance between the previous and next prime. See A267291 for primes which are at 2/3 between their neighbors. - _M. F. Hasler_, Jan 12 2016
%H Robert Israel, <a href="/A194581/b194581.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1)=3 (=(2*2+5)/3), a(2)=7 (=(2*5+11)/3), a(3)=13 (=(2*11+17)/3).
%p Primes:= select(isprime, [2,seq(i,i=3..10^4,2)]):
%p Gaps:= Primes[2..-1]-Primes[1..-2]:
%p Primes[select(t -> 2*Gaps[t-1] = Gaps[t],[$2..nops(Gaps)])]; # _Robert Israel_, Jan 03 2016
%t Table[(2 Prime[k - 1] + Prime[k + 1])/3, {k, 2, 360}] /. {_Rational -> Nothing, n_ /; CompositeQ@ n -> Nothing} (* _Michael De Vlieger_, Jan 09 2016 *)
%o (PARI) for(k=2, 1000, q=2*prime(k-1)+prime(k+1); if(q%3==0 && isprime(q\3), print1(q\3, ", "))) \\ _Colin Barker_, Jun 27 2014
%o (PARI) A194581(n,show=0,o=2,g=0)={forprime(p=o+1,,g*2==(g=-o+o=p)||next; show&&print1(p-g",");n--||return(p-g))} \\ 2nd & 3rd optional args allow printing the whole list and using another starting value. - _M. F. Hasler_, Jan 12 2016
%Y Cf. A000040, A001223, A062234.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Aug 29 2011
%E Entries corrected by _R. J. Mathar_, Sep 30 2011