A361759 Sum of b(i) where the first b terms are all k digits of n, followed by Keith-like sum of the previous k digits until b(i) >= n

34, 33, 32, 44, 33, 40, 47, 54, 61, 39, 68, 75, 66, 86, 64, 76, 88, 100, 66, 73, 102, 96, 129, 99, 119, 139, 96, 108, 120, 132, 136, 117, 150, 112, 132, 152, 172, 116, 128, 140, 170, 138, 171, 204, 145, 165, 185, 205, 225, 148, 204, 159, 192, 225, 258, 178

Offset

10,1

Comments

Similar to the concept of (but not limited to) Keith numbers, form a sequence {b(i)} whose initial terms are the t digits of n, later terms given by the rule that b(i) = sum of t previous terms, until b(i) >= n.

Originally, the concept of Keith numbers did not include n < 10. This sequence follows this rule; however, a(n) is mathematically possible for n < 10: a(n) = n.

Links

Table of n, a(n) for n=10..65.

Example

For n = 15, the sequence is {1, 5, 6, 11, 17} (the first two terms being each of the two digits of 15 and the sequence stops at 17 because this is the first number that is at least n). So, a(15) = 1 + 5 + 6 + 11 + 17 = 40.

Prog

(Ruby)
def a(n)
    digits = n.to_s.chars.map(&:to_i)
    countDigits = digits.size
    until digits.last >= n do
        sum = digits.last(countDigits).sum
        digits.push(sum)
    end
    return digits.sum # Terms of this OEIS sequence
end # Diego V. G. Silva, Mar 24 2023
(PARI) a(n)={my(v=digits(n), s=vecsum(v)); while(v[#v] < n, v=concat(v[2..#v], vecsum(v)); s+=v[#v]); s} \\ Andrew Howroyd, Mar 23 2023

Crossrefs

Cf. A007629.

Sequence in context: A302209 A022990 A023476 * A104685 A204773 A291512

Adjacent sequences: A361756 A361757 A361758 * A361760 A361761 A361762

Keyword

nonn,base

Author

Diego V. G. Silva, Mar 23 2023

Status

approved