1,2

Semiprime analogy to A113320. The sequence is probably infinite, but it is hard to characterize the asymptotic cost of adding an n-th term. The ascending descending base exponent transform of semiprimes is A113173.

a(1) = 1. For n>1: a(n) = min {n>0: SUM[from i = 1 to n] (a(i))^(a(n-i+1)) is semiprime}. a(n) = min {n>0: SUM[from i = 1 to n] (a(i))^(a(n-i+1)) in A001358}.

a(1) = 1 by definition.

a(2) = 3 because 3 is the min x such that 1^x + x^1 is semiprime,

i.e. 1^3 + 3^1 = 4 = 2*2.

a(3) = 5 because 1^5 + 3^3 + 5^1 = 33 = 3 * 11 is semiprime.

a(4) = 2 because 1^2 + 3^5 + 5^3 + 2^1 = 371 = 7 * 53.

a(5) = 4 because 1^4 + 3^2 + 5^5 + 2^3 + 4^1 = 3147 = 3 * 1049.

a(6) = 2 because 1^2 + 3^4 + 5^2 + 2^5 + 4^3 + 2^1 = 205 = 5 * 41.

a(7) = 2 because 1^2 + 3^2 + 5^4 + 2^2 + 4^5 + 2^3 + 2^1 = 1673 = 7 * 239.

a(8) = 4 because 1^4 + 3^2 + 5^2 + 2^4 + 4^2 + 2^5 + 2^3 + 4^1 = 111 = 3 * 37.

Cf. A001358, A005408, A113122, A113153, A113154, A113336, A113320, A113271, A113258, A113257, A113231, A113171, A113208.

Sequence in context: A059246 A091276 A076562 this_sequence A104807 A131793 A065186

Adjacent sequences: A113472 A113473 A113474 this_sequence A113476 A113477 A113478

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 08 2006