1,2

The initial kinetic energy of the stone t is fully dissipated and the stone sinks if t=1. The length of the collisional process of the stone with "water surface" = natural numbers is t, means the stone t rebounds t-times.

Stone skipping sequences are a generalized case of scarce sequences see A137292.

L. Bocquet; The physics of stone skipping; 2003 American Association of Physics Teachers http://lpmcn.univ-lyon1.fr/~lbocquet/AJPricochets.pdf

D. X. Charles : Sieve Methods, July 2000, University of Wisconsin. http://pages.cs.wisc.edu/~cdx/Sieve.pdf

R. Eismann : Decomposition of natural numbers into weight X level + jump and application to a new classification of prime numbers, ArXiv 2008. http://arXiv.org/PS_cache/arXiv/pdf/0711/0711.0865v2.pdf

M. C. Wunderlich : A general class of sieve generated sequences, Acta Arithmetica XVI,1969, pp.41-56. http://matwbn.icm.edu.pl/ksiazki/aa/aa16/aa1614.pdf

Start with the set of natural numbers. Let a(0)= t. Jump t positions to the right, erase t positions; from the last erased position jump t-1 positions to the right, erase t-1 positions;.....; jump 1 position to the right, erase 1 position. Go to the smallest i>t. Set t=i. Repeat.

Start with natural numbers

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,...

a(0)=1 set t=1 (jump 1 position to the right, erase 1 position) gives

1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,...

i=3 set t=3 (jump 3 positions to the right, erase 3 positions; from the last erased position jump 2 positions to the right, erase 2 positions; from the last erased position jump 1 position to the right, erase 1 position) gives

1,3,4,5,9,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,...

i=4 set t=4 (jump 4 positions to the right, erase 4 positions; from the last erased position jump 3 positions to the right, erase 3 positions; from the last erased position jump 2 positions to the right, erase 2 positions;from the last erased position jump 1 position to the right, erase 1 position ) gives

1,3,4,5,9,13,18,19,23,27,28,...

i=5 set t=5

repeat procedure

Cf. A137292.

Adjacent sequences: A136256 A136257 A136258 this_sequence A136260 A136261 A136262

Sequence in context: A108018 A080633 A026488 this_sequence A099560 A050161 A117125

easy,nonn,uned

Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Mar 18 2008