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A338924
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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).
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6
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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
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OFFSET
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1,2
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COMMENTS
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This is the lexicographically earliest sequence of distinct positive terms with this property. The prime digits are 2, 3, 5 and 7.
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LINKS
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EXAMPLE
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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;
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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;
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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