A350324 - OEIS

%I #14 Feb 10 2022 22:17:09

%S 88,112,118,140,182,202,214,242,284,292,298,316,322,338,358,388,400,

%T 410,422,448,470,478,490,512,526,532,548,578,622,632,664,682,692,700,

%U 710,718,742,760,772,778,788,800,812,830,838,844,862,868,886,892,898,910,920,928,952,958,982,1000,1022,1040,1052,1072,1078,1108,1130,1136,1142,1154,1162,1172,1192,1204

%N Missing even distances in full prime rulers, i.e., even numbers k, 0 < k < p-3 for some prime p, such that k is not the difference of two primes less than or equal to p.

%C Inspired by the notion of 'distset' as in A349976, and the general idea of sets of natural numbers as marks of a 'ruler'.

%e a(1) = 88 < p - 3 for prime number p = 97, and there are no primes p1, p2 <= p with 88 = p1 - p2.

%p primedist := n -> {seq(2*j, j = 0..(ithprime(n) - 3)/2)} minus `union`(seq({seq(abs(ithprime(j) - ithprime(k)), k = 1..j)}, j = 1..n)):

%p `union`(seq(primedist(j), j = 1..200)); # _Peter Luschny_, Dec 24 2021

%o (PARI) genit(maxx=1300)={arr=List();forstep(x=2,maxx,2,q=nextprime(x+2);if(!isprime(q-x),listput(arr,x)));arr;} \\ _Bill McEachen_, Feb 09 2022

%Y Cf. A000230, A001223, A071904, A349976.

%K nonn

%O 1,1

%A _Rainer Rosenthal_, Dec 24 2021