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

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. The nonprime digits are 0, 1, 4, 6, 8 and 9.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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