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

1,3

Comments

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

Links

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A186330 A153809 A355330 * A360126 A004274 A004280

Adjacent sequences: A338920 A338921 A338922 * A338924 A338925 A338926

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Nov 15 2020

Status

approved