

A355975


a(1) = 1. For n >= 2, add to a(n1) its prime or nonprime index to obtain a(n).


0



1, 2, 3, 5, 8, 12, 19, 27, 45, 76, 131, 163, 201, 356, 641, 757, 891, 1628, 2998, 5567, 10400, 19526, 36838, 69770, 132623, 145002, 276582, 528994, 1014241, 1948927, 2094369, 4033308, 7781263, 15036531, 29100147, 56394812, 109429140, 212585890, 413435408, 804856919, 846240101
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OFFSET

1,2


COMMENTS

Two separate indices determine the progress of this sequence, like two parallel scales. What regularities or irregularities in the distribution of primes and nonprimes among the terms may emerge as the sequence grows?


LINKS



EXAMPLE

Start with 1. As a nonprime, its index is 1. Add up the term and its index to get the next term, 2. This is a prime whose appropriate index is 1. The third term therefore is 2 + 1 = 3. And so on.
a(n) Prime index Nonprime index
1  1
2 1 
3 2 
5 3 
8  4
12  7
19 8 
.............................


PROG

(PARI) first(n) = { n = max(n, 1); print1(1", "); res = vector(n); res[1] = 1; for(i = 2, n, if(!isprime(res[i1]), res[i] = 2*res[i1]  primepi(res[i1]) , res[i] = res[i1] + primepi(res[i1]) ); print1(res[i]", "); ); res } \\ David A. Corneth, Jul 26 2022


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



