A339091 a(1)=a(2)=1; thereafter if n is even, a(n) is the cumulative sum of the odd digits so far; and if n is odd, a(n) is the cumulative sum of the even digits so far.

1, 1, 0, 2, 2, 2, 6, 2, 14, 3, 18, 7, 26, 14, 38, 18, 54, 24, 64, 24, 80, 24, 94, 33, 98, 48, 118, 50, 126, 56, 140, 62, 152, 68, 168, 69, 188, 79, 204, 95, 210, 110, 212, 113, 216, 119, 224, 130, 232, 137, 236, 151, 244, 158, 262, 164, 282, 165, 300, 174, 304, 185, 316, 195, 322, 213, 328, 220, 342, 223

Offset

1,4

Comments

The first term of the sequence, a(1), is called "the seed".

Links

Carole Dubois, Table of n, a(n) for n = 1..5001

Example

As n=7 is odd, a(7) = sum of all even digits to the left of a(7) = 0 + 2 + 2 + 2 = 6;
as n=8 is even, a(8) = the sum of all odd digits to the left of a(8) = 1 + 1 = 2);
as n=9 is odd, a(9) = the sum of all even digits to the left of a(9) =  0 + 2 + 2 + 2 + 6 + 2 = 14; etc.

Mathematica

Block[{a = {1}, s}, Array[Set[s[#], 0] &, 9]; Do[(MapIndexed[AddTo[s[First[#2]], #1] &, #]; AppendTo[a, Total@ Map[# s[#] &, If[EvenQ@ i, {2, 4, 6, 8}, {1, 3, 5, 7, 9}]]]) &@ Most@ DigitCount@ Last@ a, {i, 69}]; a ] (* Michael De Vlieger, Dec 10 2020 *)

Prog

(PARI) sumo(d) = sum(k=1, #d, if (d[k] % 2, d[k]));
sume(d) = sum(k=1, #d, if (!(d[k] % 2), d[k]));
esum(va, k) = sum(i=1, k, sumo(digits(va[i])));
osum(va, k) = sum(i=1, k, sume(digits(va[i])));
lista(nn) = {my(va = vector(nn)); va[1] = 1; va[2] = 1; for (n=3, nn, va[n] = if (n % 2, osum(va, n-1), esum(va, n-1)); ); va; } \\ Michel Marcus, Dec 10 2020
(Python)
def aupto(nn):
  seed, s = 1, [0, 0]
  alst = [None, seed]
  for n in range(2, nn+1):
    s[0] += sum(int(d) for d in str(alst[-1]) if d in "02468")
    s[1] += sum(int(d) for d in str(alst[-1]) if d in "13579")
    alst.append(s[not n%2])
  return alst[1:] # use alst[n] for a(n)
print(aupto(70)) # Michael S. Branicky, Dec 11 2020

Crossrefs

Cf. A339092, A339093 (the "sterile" seeds); A339111 (the "fertile" seeds).

Sequence in context: A230940 A110512 A078020 * A097521 A081668 A126615

Adjacent sequences: A339088 A339089 A339090 * A339092 A339093 A339094

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Nov 23 2020

Status

approved