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

1,2

Comments

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

Links

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

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

Adjacent sequences: A338921 A338922 A338923 * A338925 A338926 A338927

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Nov 15 2020

Status

approved