A299143 a(n) is the least k > n such that gcd(k,n) > 1 and gcd(k+1,n+1) > 1.
8, 9, 14, 15, 20, 21, 14, 15, 32, 33, 38, 39, 20, 21, 50, 51, 56, 57, 26, 27, 68, 69, 34, 35, 32, 33, 86, 87, 92, 93, 38, 39, 44, 45, 110, 111, 44, 45, 122, 123, 128, 129, 50, 51, 140, 141, 62, 63, 56, 57, 158, 159, 64, 65, 62, 63, 176, 177, 182, 183, 68, 69
Offset: 2
Keywords
Examples
8 is the least k>2 such that gcd(8,2)>1 and gcd(9,3)>1. So a(2)=8. 15 is the least k>9 such that gcd(15,9)>1 and gcd(16,10)>1. Therefore a(9)=15.
Links
- Robert Israel, Table of n, a(n) for n = 2..10000
Programs
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Maple
f:= proc(n) local k; for k from n+1 do if igcd(k,n)>1 and igcd(k+1,n+1)>1 then return k fi od end proc: map(f, [$2..100]); # Robert Israel, Mar 08 2018 -
Mathematica
Array[Block[{k = # + 1}, While[Or[CoprimeQ[#, k], CoprimeQ[# + 1, k + 1]], k++]; k] &, 62, 2] (* Michael De Vlieger, Feb 03 2018 *) -
PARI
a(n) = for (k=n+1, oo, if (gcd(n,k)>1 && gcd(n+1, k+1)>1, return (k))) \\ Rémy Sigrist, Feb 04 2018
Formula
From Rémy Sigrist, Feb 04 2018: (Start)
a(p) = 3 * p for any odd prime p.
a(2*k + 1) = a(2*k) + 1 for any k > 0.
a(n) = n + 2*A172170(n + 1) for any n > 1.
(End)