A352960 The successive digits of the sequence are the successive digital roots of a(n) + a(n+1).

1, 9, 18, 19, 7, 3, 6, 28, 2, 4, 16, 37, 46, 12, 25, 8, 13, 21, 55, 5, 14, 15, 23, 27, 17, 11, 64, 73, 36, 32, 45, 41, 59, 26, 29, 39, 35, 22, 34, 54, 82, 24, 31, 33, 63, 49, 48, 72, 57, 66, 81, 38, 47, 75, 91, 99, 68, 58, 43, 44, 84, 42, 51, 93, 117, 77, 69, 86, 52, 78, 53, 95, 111, 62, 129, 118, 56

Offset

1,2

Comments

This is the lexicographically earliest sequence of distinct positive terms with the property.

No zero is in the sequence as zero cannot be a digital root (DR in short hereunder).

Links

Thomas Scheuerle, Table of n, a(n) for n = 1..6000

Example

a(1) + a(2) = 1 + 9 = 10 with DR = 1;
a(2) + a(3) = 9 + 18 = 27 with DR = 9;
a(3) + a(4) = 18 + 19 = 37 with DR = 1;
a(4) + a(5) = 19 + 7 = 26 with DR = 8;
a(5) + a(6) = 7 + 3 = 10 with DR = 1;
a(6) + a(7) = 3 + 6 = 9 with DR = 9;
a(7) + a(8) =  6 + 28 = 34 with DR = 7;
a(8) + a(9) =  28 + 2 = 30 with DR = 3;
a(9) + a(10) = 2 + 4 = 6 with DR = 6;
a(10) + a(11) = 4 + 16 = 20 with DR = 2;
a(11) + a(12) = 16 + 37 = 53 with DR = 8; etc.
We see that the succession of the above DRs is the succession of the digits of the sequence (1, 9, 1, 8, 1, 9, 7, 3, 6, 2, 8, ...)

Prog

(MATLAB)
function a = A352960( max_n )
    ad(1) = 1;
    a(1) = 1;
    for n = 2:max_n
        k = 1;
        while 0 == check_k(a(n-1), k, a, ad(n-1))
            k = k + 1;
        end
        a(n) = k;
        s = num2str(k);
        for m = 1:length(s)
            ad = [ad str2num(s(m))];
        end
    end
end
function ok = check_k(m, k, a, d)
    dr = 1+mod(m+k-1, 9);
    ok = (d == dr) && isempty(find(a==k, 1)) ...
    && isempty(find(num2str(k)=='0', 1));
end % Thomas Scheuerle, Apr 11 2022

Crossrefs

Cf. A010888.

Sequence in context: A250769 A158908 A202188 * A060993 A352380 A297267

Adjacent sequences: A352957 A352958 A352959 * A352961 A352962 A352963

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Apr 11 2022

Status

approved