A339077 Numbers k such that k and k+1 are both coprime to their digital sum (A339076).

10, 13, 16, 31, 34, 37, 52, 58, 73, 91, 94, 97, 100, 103, 106, 121, 124, 127, 142, 148, 160, 163, 166, 181, 184, 187, 211, 214, 217, 232, 238, 250, 253, 256, 271, 274, 277, 289, 292, 295, 298, 301, 304, 340, 343, 346, 361, 367, 379, 382, 385, 388, 412, 418, 430

Offset: 1

Author

Amiram Eldar, Nov 22 2020

Keywords

• nonn
• base

Comments

Cooper and Kennedy (1997) noted that this sequence is infinite since 10^k is a term for all k>=1. They also noted that there can be no more than 2 consecutive numbers that are coprime to their digital sum since if 3|k then 3|A007953(k).

Examples

			10 is a term since gcd(10, A007953(10)) = 1 and gcd(11, A007953(11)) = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Curtis Cooper and Robert E. Kennedy, On the set of positive integers which are relatively prime to their digital sum and its complement, J. Inst. Math. & Comp. Sci. (Math. Ser.), Vol. 10 (1997), pp. 173-180.

Crossrefs

Cf. A007953, A339076.

Programs

Mathematica

q[n_] := CoprimeQ[n, Plus @@ IntegerDigits[n]]; Select[Range[500], q[#] && q[# + 1] &]