login
A358975
Numbers that are coprime to their digital sum in base 3 (A053735).
4
1, 3, 5, 7, 9, 11, 13, 17, 19, 23, 27, 29, 31, 37, 41, 43, 47, 49, 51, 53, 55, 59, 61, 67, 69, 71, 73, 79, 81, 83, 85, 89, 91, 97, 101, 103, 107, 109, 113, 119, 121, 123, 125, 127, 129, 131, 137, 139, 141, 143, 147, 149, 151, 153, 155, 157, 159, 161, 163, 167, 169
OFFSET
1,2
COMMENTS
Numbers k such that gcd(k, A053735(k)) = 1.
All the terms are odd since if k is even then A053735(k) is even and so gcd(k, A053735(k)) >= 2.
Olivier (1975, 1976) proved that the asymptotic density of this sequence is 4/Pi^2 = 0.40528... (A185199).
The powers of 3 (A000244) are terms. These are also the only ternary Niven numbers (A064150) in this sequence.
Includes all the odd prime numbers (A065091).
LINKS
Christian Mauduit, Carl Pomerance, and András Sárközy, On the distribution in residue classes of integers with a fixed sum of digits, The Ramanujan Journal, Vol. 9, No. 1-2 (2005), pp. 45-62; alternative link.
Michel Olivier, Sur la probabilité que n soit premier à la somme de ses chiffres, C. R. Math. Acad. Sci. Paris, Série A, Vol. 280 (1975), pp. 543-545.
Michel Olivier, Fonctions g-additives et formule asymptotique pour la propriété (n, f(n)) = q, Acta Arithmetica, Vol. 31, No. 4 (1976), pp. 361-384; alternative link.
EXAMPLE
3 is a term since A053735(3) = 1, and gcd(3, 1) = 1.
MATHEMATICA
q[n_] := CoprimeQ[n, Plus @@ IntegerDigits[n, 3]]; Select[Range[200], q]
PROG
(PARI) is(n) = gcd(n, sumdigits(n, 3)) == 1;
CROSSREFS
Subsequences: A000244, A065091.
Similar sequences: A094387, A339076, A358976, A358977, A358978.
Sequence in context: A326581 A050150 A062090 * A345898 A172095 A309361
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Dec 07 2022
STATUS
approved