A338924 - OEIS

%I #11 Nov 23 2020 06:02:36

%S 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,

%T 34,35,36,38,39,40,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,63,

%U 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

%N 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).

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

%H Carole Dubois, <a href="/A338924/b338924.txt">Table of n, a(n) for n = 1..9999</a>

%e 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;

%e a(2) = 2 as 2 (a prime term) is the sum of all prime digits used so far;

%e 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;

%e ...

%e a(14) = 11 (a prime term) as 11 is the sum of all prime digits used so far (2 + 2 + 5 + 2);

%e 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;

%e ...

%e 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.

%o (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

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

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Carole Dubois_, Nov 15 2020