A338922 Every odd term k of the sequence is the cumulative sum of the odd digits used so far (the digits of k are included in the sum).

1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 11, 32, 34, 36, 21, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 71, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140

Offset

1,2

Comments

This is the lexicographically earliest sequence of distinct positive terms with this property.

Links

Carole Dubois, Table of n, a(n) for n = 1..5000

Example

a(1) = 1 as the sum of all odd digits used so far is 1:
a(2) = 2 as 2 is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
a(3) = 4 as a(3) = 3 would be a contradiction and a(3) = 4 doesn't lead to a contradiction;
...
a(17) = 11 as the sum of all odd digits used so far is 11 (1 + 1 + 1 + 1 + 1 + 1 + 3 + 1 + 1); etc.

Prog

(PARI) my(v=[], S=0, p=2, n=1); while(n<100, c=0; for(q=S, p, if(q%2, m=0; for(i=1, #digits(q), if(digits(q)[i]%2, m+=digits(q)[i])); if(S+m==q&&!vecsearch(vecsort(v), q), v=concat(v, q);  S+=m; c++; break))); if(c==0, for(j=1, #digits(p), if(digits(p)[j]%2, S+=digits(p)[j])); v=concat(v, p); p+=2); n++); v \\ Derek Orr, Nov 22 2020

Crossrefs

Cf. A338923, A338924 and A338925 (variants on the same idea).

Sequence in context: A337718 A246410 A195169 * A055964 A055966 A087113

Adjacent sequences: A338919 A338920 A338921 * A338923 A338924 A338925

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Nov 15 2020

Status

approved