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

1,1

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).

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.

Example

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

Mathematica

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

Crossrefs

Cf. A007953, A339076.

Sequence in context: A055984 A282108 A306035 * A335016 A240109 A163652

Adjacent sequences: A339074 A339075 A339076 * A339078 A339079 A339080

Keyword

nonn,base

Author

Amiram Eldar, Nov 22 2020

Status

approved