A337803 Odd integers k not divisible by 5, such that dr(k) divides k-1 or k+1, where dr(k) is the additive digital root of k (A010888).

1, 11, 13, 17, 19, 29, 31, 37, 41, 43, 47, 49, 59, 67, 71, 73, 83, 89, 91, 97, 101, 103, 109, 119, 121, 127, 131, 137, 139, 143, 149, 157, 161, 163, 169, 173, 181, 191, 193, 199, 209, 211, 217, 221, 223, 227, 229, 233, 239, 247, 253, 263, 271, 281, 283, 287, 289, 299

Offset: 1

Author

Bill McEachen, Sep 22 2020

Keywords

• nonn
• base

Examples

			For k = 13, the additive digital root = 4. (12 mod 4) = 0 and (14 mod 4) = 2, and thus 13 is a sequence entry.
For k = 31, the additive digital root = 4. (30 mod 4) = 2 and (32 mod 4) = 0, so 31 is a sequence entry.
For k = 23, the additive digital root = 5. (22 mod 5) = 2 and (24 mod 5) = 4, so 23 is not a sequence entry.
		

Crossrefs

Cf. A010888 (additive digital roots).

Programs

Mathematica

Select[Range[1, 300, 2], !Divisible[#, 5] && (Divisible[# - 1, (dr = Mod[# - 1, 9] + 1)] || Divisible[# + 1, dr]) &] (* Amiram Eldar, Oct 02 2020 *)

PARI

genit(maxx)={if(maxx<11,maxx=11);for (n=1,maxx,if(n%2==0 ||n%5==0,next);dr=(n-1)%9+1;if( (n+1)%dr==0 ||(n-1)%dr==0, print1(n,",")));}