A338925 Every nonprime term k of the sequence is the cumulative sum of the nonprime digits used so far (the digits of k are included in the sum).

0, 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 25, 37, 41, 30, 34, 43, 42, 47, 53, 59, 55, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 130, 131, 133, 137, 135, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277

Offset

1,3

Comments

This is the lexicographically earliest sequence of distinct nonnegative terms with this property. The nonprime digits are 0, 1, 4, 6, 8 and 9.

Links

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

Example

a(1) = 0 as 0 (a nonprime term) is the sum of all nonprime digits used so far;
a(2) = 1 as 1 (a nonprime term) is the sum of all nonprime digits used so far (0 + 1);
a(3) = 2 as 2 (a prime term) is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
...
a(14) = 25 (a nonprime term) as 25 is the sum of all nonprime digits used so far (0 + 1 + 1 + 1 + 1 + 1 + 1 + 9 + 9 + 1);
a(15) = 37 (a prime term) as 37 is the smallest term not yet present in the sequence that doesn't lead to a contradiction; etc.

Prog

(PARI) v=[0]; w=[0]; n=1; p=1; while(n<75, for(q=vecsum(w), nextprime(p+1), if(!isprime(q), m=[]; for(k=1, #digits(q), if(!isprime(digits(q)[k]), m=concat(m, digits(q)[k]))); c=0; if(vecsum(w)+vecsum(m)==q&&!vecsearch(vecsort(v), q), v=concat(v, q); w=concat(w, m); c++; break))); if(c==0, p=nextprime(p+1); for(j=1, #digits(p), if(!isprime(digits(p)[j]), w=concat(w, digits(p)[j]))); v=concat(v, p)); n++); v \\ Derek Orr, Nov 16 2020

Crossrefs

Cf. A338922, A338923 and A338924 (variants on the same idea).

Sequence in context: A327783 A319333 A326715 * A358761 A371654 A089063

Adjacent sequences: A338922 A338923 A338924 * A338926 A338927 A338928

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Nov 15 2020

Status

approved