A339077 - OEIS

%I #8 Nov 23 2020 02:06:28

%S 10,13,16,31,34,37,52,58,73,91,94,97,100,103,106,121,124,127,142,148,

%T 160,163,166,181,184,187,211,214,217,232,238,250,253,256,271,274,277,

%U 289,292,295,298,301,304,340,343,346,361,367,379,382,385,388,412,418,430

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

%C 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).

%H Amiram Eldar, <a href="/A339077/b339077.txt">Table of n, a(n) for n = 1..10000</a>

%H Curtis Cooper and Robert E. Kennedy, <a href="http://cs.ucmo.edu/~cnc8851/articles/setcomp.pdf">On the set of positive integers which are relatively prime to their digital sum and its complement</a>, J. Inst. Math. & Comp. Sci. (Math. Ser.), Vol. 10 (1997), pp. 173-180.

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

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

%Y Cf. A007953, A339076.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Nov 22 2020