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A277831
Number of '1' digits in the set of all numbers from 0 to A014824(n) = Sum_{i=1..n} i*10^(n-i) = (0, 1, 12, 123, 1234, 12345, ...).
3
0, 1, 5, 57, 689, 8121, 93553, 1058985, 11824417, 130589849, 1429355281, 15528120716, 167626886179, 1799725651922, 19231824420465, 204663923217008, 2170096022293551, 22935528124170094, 241700960254046637, 2540466392663923180, 26639231827873799724
OFFSET
0,3
LINKS
M. F. Hasler, "Digits d in 0 through 123...n", OEIS Wiki, Nov. 2016.
FORMULA
a(n) = A277832(n) + 3*10^(n-2), for 2 <= n <= 10.
More generally, for m = 0, ..., 9, let a[m] denote A277830, ..., A277838 and A277849, respectively. Then a[0](n) = a[n](n) = a[m](n) + 1 for all m > n >= 0, and a[m-1](n) = a[m](n) + (m+1)*10^(n-m) for all n >= m > 1.
EXAMPLE
For n=2 are counted the same '1' as for n=1, plus the 4 additional digits '1' in 10, 11 and 12.
PROG
(PARI) print1(c=N=0); for(n=1, 8, print1(", "c+=sum(k=N+1, N=N*10+n, #select(d->d==1, digits(k)))))
(PARI) A277831(n)=if(n<2, n, n<11, A277832(n)+3*10^(n-2), error("n > 10 not yet implemented")) \\ M. F. Hasler, Nov 02 2016, edited Dec 28 2020
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Nov 01 2016
EXTENSIONS
More terms from Lars Blomberg, Nov 05 2016
Removed incorrect b-file. - David A. Corneth, Dec 31 2020
STATUS
approved