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

Author

Eric Angelini and Carole Dubois, Nov 15 2020

Keywords

• base
• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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