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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). 2

%I #18 Jan 16 2019 02:44:11

%S 0,8,18,26,36,54,56,74,84,86,134,140,156,168,170,174,194,200,216,224,

%T 236,240,246,260,300,308,324,326,366,368,386,390,414,420,440,456,464,

%U 476,494,498,518,536,560,564,576,590,594,624,630,650,660,678,698,708

%N 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).

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

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

%C All terms are even.

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

%H Robert Israel, <a href="/A298161/b298161.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

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

%p filter:= proc(n) local p, k;

%p p:= 1:

%p for k from 1 do

%p p:= nextprime(p);

%p if p > n+k then return true

%p elif n+k mod p = 0 then return false

%p fi

%p od

%p end proc:

%p select(filter, [seq(i,i=0..1000,2)]); # _Robert Israel_, Jan 16 2018

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

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jan 14 2018

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Last modified April 19 19:02 EDT 2024. Contains 371798 sequences. (Running on oeis4.)