A355975 a(1) = 1. For n >= 2, add to a(n-1) its prime or nonprime index to obtain a(n).

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

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

Table of n, a(n) for n=1..41.

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[i-1]), res[i] = 2*res[i-1] - primepi(res[i-1]) , res[i] = res[i-1] + primepi(res[i-1]) ); print1(res[i]", "); ); res } \\ David A. Corneth, Jul 26 2022

Crossrefs

Cf. A000040, A018252.

Sequence in context: A055804 A267372 A369696 * A327421 A124062 A274199

Adjacent sequences: A355972 A355973 A355974 * A355976 A355977 A355978

Keyword

nonn

Author

Tamas Sandor Nagy, Jul 26 2022

Extensions

a(14)-a(30) from Thomas Scheuerle, Jul 26 2022

More terms from David A. Corneth, Jul 26 2022

Status

approved