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).

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

Author

Eric Angelini and Carole Dubois, Nov 15 2020

Keywords

• base
• nonn

Comments

This is the lexicographically earliest sequence of distinct positive terms with this property. The prime digits are 2, 3, 5 and 7.

Examples

			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.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..9999

Crossrefs

Cf. A338922, A338923 and A338925 (variants on the same idea).

Programs

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