A330814 a(1) = 1; a(n+1) = Sum_{k=1..n} {q(a(k)): q(a(k)) = q(a(n))}, where q(n) = A007953(n) + A055642(n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 6, 14, 21, 10, 9, 20, 8, 18, 11, 12, 15, 16, 27, 22, 12, 20, 16, 36, 33, 24, 32, 28, 12, 25, 45, 44, 30, 30, 35, 40, 18, 55, 24, 40, 24, 48, 14, 35, 50, 42, 56, 13, 30, 40, 36, 66, 28, 36, 77, 16, 54

Offset

1,2

Comments

a(n+1) = k(n)*q(a(n)), where k(n) is the number of times (up to and including a(n)) that a term having the same q-value as a(n) has occurred in the sequence so far.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

a(2) is q(a(1))=a(1)=2; a(10)=q(10)=3, and 3=q(a(2)) has been seen once before, so a(11)=3+3=6.

Mathematica

s[n_] := Plus @@(d = IntegerDigits[n]) + Length[d]; a[1] = 1; a[n_] := a[n] = (s1 = s[a[n - 1]])*(1 + Sum[Boole[s[a[k]] == s1], {k, 1, n - 2}]); Array[a, 100] (* Amiram Eldar, Jan 01 2020 *)

Prog

(Magma) q:=func<n|&+Intseq(n)+#Intseq(n)>; a:=[1, 2]; for n in [3..70] do Append( ~a, &+[ q(a[k-1]):k in [2..n]| q(a[k-1]) eq q(a[n-1])]); end for; a; // Marius A. Burtea, Jan 02 2020

Crossrefs

Cf. A279818, A330807, A007953, A055642.

Sequence in context: A291751 A275987 A048893 * A379001 A379000 A305903

Adjacent sequences: A330811 A330812 A330813 * A330815 A330816 A330817

Keyword

nonn,base

Author

David James Sycamore, Jan 01 2020

Status

approved