A109823 a(n) is the minimal b >= n such that sum of consecutive integers from n to b is a semiprime.

3, 4, 7, 4, 8, 6, 8, 11, 9, 10, 15, 13, 16, 14, 15, 17, 18, 20, 20, 23, 21, 22, 35, 25, 25, 26, 28, 29, 32, 32, 36, 33, 33, 34, 35, 38, 42, 38, 39, 42, 45, 43, 44, 50, 46, 46, 48, 53, 49, 53, 51, 54, 56, 59, 55, 62, 57, 58, 60, 61, 62, 62, 68, 65, 65, 67, 70, 71, 69, 71, 72, 73

Offset

1,1

Comments

If n is a semiprime, a(n)=n. It is not evident that for any n there is relative a(n), see A109411. For n <1000, the corresponding a(n) exists. Cf. A109824(n) = A109823(n) - n + 1.

Links

Table of n, a(n) for n=1..72.

Mathematica

cis[n_]:=Module[{b=0}, While[PrimeOmega[(n(n+b))/2]!=2, b++]; n+b]; Array[ cis, 80] (* Harvey P. Dale, Mar 30 2014 *)

Prog

(PARI) { a(n) = my(s, m); s = n; m = n; while(bigomega(s)!=2, m++; s += m); m }

Crossrefs

Cf. A109411, A109824.

Sequence in context: A161775 A282535 A193967 * A337124 A267447 A071051

Adjacent sequences: A109820 A109821 A109822 * A109824 A109825 A109826

Keyword

nonn

Author

Zak Seidov & Max Alekseyev, Jul 03 2005

Status

approved