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A267291 Primes which are at 2/3 of the distance between their neighbors. 1

%I #10 Jan 13 2016 00:09:26

%S 11,17,41,71,97,101,107,197,227,281,311,397,457,461,487,499,617,769,

%T 827,857,881,937,1091,1301,1427,1447,1451,1487,1543,1567,1579,1667,

%U 1697,1787,1871,1877,1901,1997,2087,2141,2381,2411,2539,2609,2617,2687,2707,2711,2749,2801,3019,3061,3109,3167,3181,3203,3217,3257

%N Primes which are at 2/3 of the distance between their neighbors.

%C Or: primes p such that p = (prevprime(p) + 2 nextprime(p))/3, Or, p=prime(k) such that prime(k)-prime(k-1) = 2(prime(k+1)-prime(k)). See A194581 for primes which are at 1/3 of the distance between their neighbors.

%e 11 is in the sequence because 11 = (7 + 2*13) / 3.

%t Select[Prime@ Range@ 480, # == (NextPrime[#, -1] + 2 NextPrime@ #)/3 &] (* _Michael De Vlieger_, Jan 12 2016 *)

%o (PARI) a(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.

%Y Cf. A194581.

%K nonn

%O 1,1

%A _M. F. Hasler_, Jan 12 2016

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