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A280055 Nachos sequence based on 1 plus primes (A008578).

%I A280055 #19 Mar 05 2017 15:13:56
%S A280055 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 A280055 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 A280055 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 A280055 Nachos sequence based on 1 plus primes (A008578).
%C A280055 Like A280053 but based on 1,2,3,5,7,11,... rather than squares. See that entry for further information.
%C A280055 Equivalently, greedily subtract terms of A014284 from n until reaching 0; a(n) = number of steps required.
%H A280055 Lars Blomberg, <a href="/A280055/b280055.txt">Table of n, a(n) for n = 1..10000</a>
%e A280055 26 takes 4 phases to read 0:
%e A280055 subtract leaves
%e A280055 1   25
%e A280055 2   23
%e A280055 3   20
%e A280055 5   15
%e A280055 7   8
%e A280055 ------
%e A280055 1   7
%e A280055 2   5
%e A280055 3   2
%e A280055 ------
%e A280055 1   1
%e A280055 ------
%e A280055 1   0
%e A280055 so a(26) = 4
%p A280055 A280055 := proc(n)
%p A280055     local a,nres,i ;
%p A280055     a := 0 ;
%p A280055     nres := n;
%p A280055     while nres > 0 do
%p A280055         for i from 1 do
%p A280055             if A014284(i) > nres then
%p A280055                 break;
%p A280055             end if;
%p A280055         end do:
%p A280055         nres := nres-A014284(i-1) ;
%p A280055         a := a+1 ;
%p A280055     end do:
%p A280055     a ;
%p A280055 end proc:
%p A280055 seq(A280055(n),n=1..80) ; # _R. J. Mathar_, Mar 05 2017
%Y A280055 Cf. A280055, A014284.
%Y A280055 For records see A280760.
%K A280055 nonn
%O A280055 1,2
%A A280055 _N. J. A. Sloane_, Jan 08 2017