A244158 If n = Sum c_i * 10^i then a(n) = Sum c_i * Cat(i+1), where Cat(k) = A000108(k).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 5

Offset: 0

Author

Antti Karttunen, Jun 22 2014

Keywords

• nonn
• base
• less

Comments

This sequence converts any number from various "Catalan Base number systems" (when represented as decimal numbers) back to the integer the numeral represents: e.g. we have a(A014418(n)) = n and a(A244159(n)) = n (except for the latter this is eventually broken by the shortcomings of the decimal representation used, while for the former it works for all n, because no digits larger than 3 will ever appear in the terms of A014418).

A197433 is similar, but replaces 2^k with A000108(k+1) in binary expansion of n.

For 1- and 2-digit numbers the same as A156230. - R. J. Mathar, Jun 27 2014

Links

• Index entries for sequences related to decimal expansion of n

Crossrefs

Cf. A000108, A014418, A244159, A197433, A244155, A244156, A244157.

Differs from A028897 and A081594 for the first time at n=100, which here is a(100) = 5.

Programs

Maple

A244158 := proc(n)
    local dgs,k ;
    dgs := convert(n,base,10) ;
    add( op(k,dgs)*A000108(k),k=1..nops(dgs)) ;
end proc: # R. J. Mathar, Jan 31 2015