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A350324
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.
0
88, 112, 118, 140, 182, 202, 214, 242, 284, 292, 298, 316, 322, 338, 358, 388, 400, 410, 422, 448, 470, 478, 490, 512, 526, 532, 548, 578, 622, 632, 664, 682, 692, 700, 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
OFFSET
1,1
COMMENTS
Inspired by the notion of 'distset' as in A349976, and the general idea of sets of natural numbers as marks of a 'ruler'.
EXAMPLE
a(1) = 88 < p - 3 for prime number p = 97, and there are no primes p1, p2 <= p with 88 = p1 - p2.
MAPLE
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)):
`union`(seq(primedist(j), j = 1..200)); # Peter Luschny, Dec 24 2021
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Rainer Rosenthal, Dec 24 2021
STATUS
approved