A280055 - OEIS

%I #19 Mar 05 2017 15:13:56

%S 1,2,1,2,3,1,2,3,2,3,1,2,3,2,3,4,2,1,2,3,2,3,4,2,3,4,3,4,1,2,3,2,3,4,

%T 2,3,4,3,4,2,3,1,2,3,2,3,4,2,3,4,3,4,2,3,4,3,4,5,1,2,3,2,3,4,2,3,4,3,

%U 4,2,3,4,3,4,5,3,2,1,2,3,2,3,4,2,3,4,3,4,2,3,4,3,4,5,3,2,3,4,3

%N Nachos sequence based on 1 plus primes (A008578).

%C Like A280053 but based on 1,2,3,5,7,11,... rather than squares. See that entry for further information.

%C Equivalently, greedily subtract terms of A014284 from n until reaching 0; a(n) = number of steps required.

%H Lars Blomberg, <a href="/A280055/b280055.txt">Table of n, a(n) for n = 1..10000</a>

%e 26 takes 4 phases to read 0:

%e subtract leaves

%e 1   25

%e 2   23

%e 3   20

%e 5   15

%e 7   8

%e ------

%e 1   7

%e 2   5

%e 3   2

%e ------

%e 1   1

%e ------

%e 1   0

%e so a(26) = 4

%p A280055 := proc(n)

%p     local a,nres,i ;

%p     a := 0 ;

%p     nres := n;

%p     while nres > 0 do

%p         for i from 1 do

%p             if A014284(i) > nres then

%p                 break;

%p             end if;

%p         end do:

%p         nres := nres-A014284(i-1) ;

%p         a := a+1 ;

%p     end do:

%p     a ;

%p end proc:

%p seq(A280055(n),n=1..80) ; # _R. J. Mathar_, Mar 05 2017

%Y Cf. A280055, A014284.

%Y For records see A280760.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jan 08 2017