A338941 a(1)=1. For n >= 2, let S be the sum of all prime digits in a(1), a(2), ... a(n-1) and let C be the next nonprime number not already in the sequence. If S is a prime less than C and is not already a term of the sequence, a(n) = S. Otherwise, a(n) = C.

1, 4, 6, 8, 9, 10, 12, 2, 14, 15, 16, 18, 20, 11, 21, 13, 22, 24, 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

Offset

1,2

Comments

Similar to A338924, however this sequence does not account for the prime digits of a(n) itself.

Each prime term is the sum of all prime digits of each previous term.

Links

Table of n, a(n) for n=1..69.

Example

a(16) = 13 because the sum of the prime digits from the previous terms is 2+2+5+2+2 = 13 (a prime) and 13 is less than the next nonprime (22).
a(17) = 22 because the sum of the prime digits from the previous terms is 2+2+5+2+2+3 = 16 (a nonprime), so a(17) is the next nonprime in the sequence.
a(18) = 24 because the sum of the prime digits from the previous terms is 2+2+5+2+2+3+2+2 = 20 (a nonprime).
a(16) = 25 because the sum of the prime digits from the previous terms is 2+2+5+2+2+3+2+2+2 = 22 (a nonprime).
a(17) = 26 because the sum of the prime digits from the previous terms is 2+2+5+2+2+3+2+2+2+2+5 = 29 (a prime) but it is not less than the next nonprime (which is 26).

Prog

(PARI) a(n)=my(v=[1], S=0, k=1, C=4, m); while(k<n, while(isprime(C), C++); m=vecsum(select(isprime, digits(S))); if(isprime(S) && (S<C) && !vecsearch(vecsort(v), S), v=concat(v, S); S+=m, S+= vecsum(select(isprime, digits(C))); v=concat(v, C); C++); k++); v[#v]

Crossrefs

Cf. A338924.

Sequence in context: A085558 A084984 A104499 * A137353 A336371 A167376

Adjacent sequences: A338938 A338939 A338940 * A338942 A338943 A338944

Keyword

nonn,base

Author

Eric Angelini and Derek Orr, Nov 17 2020

Status

approved