A298161 Nonnegative numbers n such that for any k > 0, n + k is not a multiple of prime(k) (where prime(k) denotes the k-th prime).

0, 8, 18, 26, 36, 54, 56, 74, 84, 86, 134, 140, 156, 168, 170, 174, 194, 200, 216, 224, 236, 240, 246, 260, 300, 308, 324, 326, 366, 368, 386, 390, 414, 420, 440, 456, 464, 476, 494, 498, 518, 536, 560, 564, 576, 590, 594, 624, 630, 650, 660, 678, 698, 708

Offset: 1

Author

Rémy Sigrist, Jan 14 2018

Keywords

• nonn

Comments

Equivalently, these are the numbers n >= 0 such that A298155(n) = 1.

Equivalently, these are the numbers n >= 0 such that the diagonal of A060175 starting at A060175(n+1, 1) contains only zeros.

All terms are even.

This sequence is a subsequence of A005843, A007494, A047207 and A047318.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005843, A007494, A007814, A007949, A047207, A047318, A060175, A112765, A214411, A298155.

Programs

Maple

filter:= proc(n) local p, k;
  p:= 1:
  for k from 1 do
    p:= nextprime(p);
    if p > n+k then return true
    elif n+k mod p = 0 then return false
    fi
  od
end proc:
select(filter, [seq(i,i=0..1000,2)]); # Robert Israel, Jan 16 2018

Formula

A007814(a(n) + 1) = 0.

A007949(a(n) + 2) = 0.

A112765(a(n) + 3) = 0.

A214411(a(n) + 4) = 0.