A136110 Limiting sequence when we start with the positive integers (A000027) and delete in step n >= 1 the term at position n + tau(a(n)), where tau(k) is the number of divisors of k.
1, 3, 4, 6, 7, 9, 12, 13, 15, 17, 18, 22, 23, 24, 28, 29, 30, 32, 33, 36, 37, 38, 43, 44, 47, 49, 51, 52, 55, 56, 58, 59, 62, 65, 66, 68, 70, 72, 73, 74, 78, 79, 80, 84, 85, 86, 88, 90, 92, 94, 96, 97, 98, 104, 105, 106, 108, 109, 111, 116, 118, 119, 121, 122, 126, 129, 130
Offset: 1
Examples
First few steps are: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,... n = 1; delete term at position 1+tau(1) = 1+1 =2: 2; 1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,... n = 2; delete term at position 2+tau(3) = 1+2 = 3: 5; 1,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,... n = 3; delete term at position 3+tau(4) = 3+3 = 6: 8; 1,3,4,6,7,9,10,11,12,13,14,15,16,17,18,19,20,... n = 4; delete term at position 4+tau(6) = 4+4 = 8: 11; 1,3,4,6,7,9,10,12,13,14,15,16,17,18,19,20,... n = 5; delete term at position 5+tau(7) = 5+2 = 7: 10; 1,3,4,6,7,9,12,13,14,15,16,17,18,19,20,... n = 6; delete term at position 6+tau(9) = 6+3 = 9: 14; 1,3,4,6,7,9,12,13,15,16,17,18,19,20,...
Links
- D. X. Charles, Sieve Methods, July 2000, University of Wisconsin.
- Rémi Eismann, Decomposition into weight * level + jump and application to a new classification of primes, arXiv:0711.0865 [math.NT]
- M. C. Wunderlich, A general class of sieve generated sequences, Acta Arithmetica XVI,1969, pp.41-56.
- Index entries for sequences generated by sieves
Extensions
Edited and extended by Klaus Brockhaus, Apr 03 2008
Moved references to the Links section R. J. Mathar, Oct 23 2009
Comments