A338923 Every even term k of the sequence is the cumulative sum of the even digits used so far (the digits of k are included in the sum).

0, 1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 10, 12, 29, 31, 33, 35, 37, 39, 41, 20, 43, 45, 47, 49, 40, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 75, 77, 79, 80, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 130

Offset: 1

Author

Eric Angelini and Carole Dubois, Nov 15 2020

Keywords

• base
• nonn

Comments

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

Examples

			a(1) = 0 as 0 is the sum of all even digits used so far:
a(2) = 1 as 1 is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
a(3) = 2 as 2 is the sum of all even digits used so far (0 + 2);
a(4) = 3 as 3 is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
...
a(17) = 10 as 10 is the sum of all even digits used so far (0 + 2 + 2 + 2 + 2 + 2 + 0);
a(18) = 12 as 12 is the sum of all even digits used so far (0 + 2 + 2 + 2 + 2 + 2 + 0 + 2);
a(19) = 29 as 29 is the smallest term not yet present in the sequence that doesn't lead to a contradiction; etc.
		

Links

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

Crossrefs

Cf. A338922, A338924 and A338925 (variants on the same idea).

Programs

PARI

my(v=[], S=0,p=1, 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