A260586 Concatenated sums of pairs of adjacent digits in the concatenation of the numbers from 1 to n.

0, 0, 3, 35, 357, 3579, 357911, 35791113, 3579111315, 357911131517, 357911131517101, 35791113151710112, 3579111315171011223, 357911131517101122334, 35791113151710112233445, 3579111315171011223344556, 357911131517101122334455667, 35791113151710112233445566778

Offset

0,3

Comments

The underlying sequence to calculate the sums of the pairs of adjacent digits is A007908 = (0, 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 12345678910, 1234567891011, ...).

Links

Harvey P. Dale, Table of n, a(n) for n = 0..292

Example

For n=3, A007908(3) is 123, and (1+2)_(2+3) gives 35, so a(3)=35.
For n=4, A007908(4) is 1234, and (1+2)_(2+3)_(3+4) gives 357, so a(4)=357.

Mathematica

Table[FromDigits[Flatten[IntegerDigits/@Total/@Partition[Flatten[ IntegerDigits/@ Range[n]], 2, 1]]], {n, 0, 20}] (* Harvey P. Dale, Dec 18 2019 *)

Prog

(PARI) b(n)=my(s=""); for(k=1, n, s=Str(s, k)); eval(s);
a(n) = {my(x = b(n)); if (x==0, d = [0], d = digits(x)); my(s=""); for (k=1, #d-1, s = concat(s, d[k] + d[k+1]); ); if (!#s, 0, eval(s)); } \\ Michel Marcus, Jul 30 2015

Crossrefs

Cf. A007908.

Sequence in context: A198961 A112488 A221922 * A089933 A086043 A221774

Adjacent sequences: A260583 A260584 A260585 * A260587 A260588 A260589

Keyword

easy,base,nonn,less

Author

Marco Ripà, Jul 29 2015

Status

approved