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.

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'.

Links

Table of n, a(n) for n=1..72.

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

Cf. A000230, A001223, A071904, A349976.

Sequence in context: A215830 A216873 A114166 * A183186 A161194 A196581

Adjacent sequences: A350321 A350322 A350323 * A350325 A350326 A350327

Keyword

nonn

Author

Rainer Rosenthal, Dec 24 2021

Status

approved