

A338938


a(1)=0. For n >= 2, let S be the sum of all nonprime digits in a(1), a(2), ... a(n1) and let P be the next prime not already in the sequence. If S is a nonprime number less than P and not already in the sequence, a(n) = S. Otherwise, a(n) = P.


1



0, 2, 3, 5, 7, 11, 13, 17, 4, 8, 16, 19, 23, 29, 31, 37, 41, 43, 47, 53, 56, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Similar to A338925, however this sequence does not include the nonprime digits of a(n) itself.
Each nonprime term is the sum of all nonprime digits of each previous term.


LINKS

Table of n, a(n) for n=1..60.


EXAMPLE

a(9) = 4 since the sum of the nonprime digits of the previous terms is 1+1+1+1 = 4 and 4 is less than the next prime, 19.
a(10) = 8 since the sum of nonprime digits of the previous terms is 1+1+1+1+4 = 8 and 8 is less than the next prime, 19.
a(11) = 16 since the sum of the nonprime digits of the previous terms is 1+1+1+1+4+8 = 16 and 16 is less than the next prime, 19.
Now, the sum of the nonprime digits of the previous terms is 1+1+1+1+4+8+1+6 = 23 (a prime number). So a(12) is the next prime number in that hasn't appeared, meaning a(12) = 19.


PROG

(PARI) my(v=[0], w=[0], n=1, p=1, m, c); while(n<125, q=vecsum(w); m=[]; p=nextprime(p); c=0; for(k=1, #digits(q), if(!isprime(digits(q)[k]), m=concat(m, digits(q)[k]))); if(!isprime(q)&&(q<p)&& !vecsearch(vecsort(v), q), v=concat(v, q); w=concat(w, m); c++); if(c==0, for(j=1, #digits(p), if(!isprime(digits(p)[j]), w=concat(w, digits(p)[j]))); v=concat(v, p); p++); n++); v


CROSSREFS

Cf. A338925.
Sequence in context: A033633 A242119 A308505 * A249823 A171049 A171053
Adjacent sequences: A338935 A338936 A338937 * A338939 A338940 A338941


KEYWORD

nonn,base


AUTHOR

Eric Angelini and Derek Orr, Nov 16 2020


STATUS

approved



