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A339077 Numbers k such that k and k+1 are both coprime to their digital sum (A339076). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 26 02:10 EDT 2021. Contains 346294 sequences. (Running on oeis4.)