login
A338924
Every prime term k of the sequence is the cumulative sum of the prime digits used so far (the digits of k are included in the sum).
6
1, 2, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 11, 21, 22, 24, 19, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100
OFFSET
1,2
COMMENTS
This is the lexicographically earliest sequence of distinct positive terms with this property. The prime digits are 2, 3, 5 and 7.
LINKS
EXAMPLE
a(1) = 1 as 1 (a nonprime term) is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
a(2) = 2 as 2 (a prime term) is the sum of all prime digits used so far;
a(3) = 4 (a nonprime term) as a(3) = 3 (a prime) would be a contradiction and a(3) = 4 doesn't lead to a contradiction;
...
a(14) = 11 (a prime term) as 11 is the sum of all prime digits used so far (2 + 2 + 5 + 2);
a(15) = 21 (a nonprime term) as 21 is the smallest term not yet present in the sequence that doesn't lead to a contradiction;
...
a(18) = 19 (a prime term) as 19 is the sum of all prime digits used so far (2 + 2 + 5 + 2 + 2 + 2 + 2 + 2); etc.
PROG
(PARI) v=[1]; w=[]; n=1; p=2; while(n<100, for(q=vecsum(w), p, if(isprime(q), m=[]; m=select(isprime, digits(q)); 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, while(isprime(p), p++); w=concat(w, select(isprime, digits(p))); v=concat(v, p); p++); n++); v \\ Derek Orr, Nov 17 2020
CROSSREFS
Cf. A338922, A338923 and A338925 (variants on the same idea).
Sequence in context: A192515 A189466 A085492 * A065090 A371167 A324560
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Carole Dubois, Nov 15 2020
STATUS
approved