login
A330070
a(n) is the smallest integer k > 1 such that k cannot be expressed as a sum of distinct earlier terms nor is a multiple of any earlier term.
3
2, 3, 7, 11, 17, 25, 59, 67, 185, 193, 563, 571, 1697, 1747, 5141, 5149, 11995, 25727, 27439, 78893, 82345, 240131, 243583, 723845, 727297, 2174987, 2178439, 6530119, 6530123, 13061947, 19590377, 39182441, 52242689, 91425127, 195910507, 235092943, 626913953
OFFSET
1,1
COMMENTS
Conjecture: Composite terms k greater than 25 will have either two or six nontrivial divisors (that is, divisors d with 1 < d < k).
The total numbers of divisors of the first 31 terms are 2, 2, 2, 2, 2, 3, 2, 2, 4, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2, 8, 2, 2, 8, 2, 4, 2, 8, 4, 2, 2. - N. J. A. Sloane, Dec 01 2019
LINKS
Rémy Sigrist and Giovanni Resta, Table of n, a(n) for n = 1..48
EXAMPLE
a(6) = 25 = 5 * 5: 5 is not in the sequence, and no combination of 2, 3, 7, 11, and 17 sums to 25.
PROG
(C++) See Links section.
CROSSREFS
Sequence in context: A045325 A216825 A094066 * A350839 A161921 A060341
KEYWORD
nonn
AUTHOR
J. Stauduhar, Nov 30 2019
EXTENSIONS
Terms a(24)-a(31) from Christian Lawson-Perfect, Dec 01 2019
Terms a(32)-a(37) from Rémy Sigrist, Dec 02 2019
STATUS
approved