|
%I #10 Jan 18 2018 07:24:51
%S 1,2,3,4,5,6,8,16,24,32,40,48,49,56,57,58,59,60,61,62,65,73,81,89,97,
%T 98,106,112,113,114,115,116,117,118,122,130,138,146,147,155,163,168,
%U 169,170,171,172,173,174,179,187,195,196,204,212,220,224,225,226
%N Numbers whose base-7 digits d(m), d(m-1),..., d(0) have m=0 or else d(i) = d(i+1) for some i in {0,1,...,m-1}.
%C These numbers comprise the complement of the set of numbers in the union of A297137 and A297138.
%C Differs from A044818 first for 344 = 1001_7. 1001_7 has two runs of length 1 and is not in A044818, but it has a sequence of two consecutive zeros and is in this sequence. - _R. J. Mathar_, Jan 18 2018
%e Base-7 digits of 4998: 2,0,4,0,0, so that 4998 is in the sequence.
%p read("transforms") :
%p isA297139 := proc(n)
%p local dgs,ud;
%p dgs := convert(n,base,7) ;
%p if nops(dgs) < 2 then
%p return true;
%p end if;
%p if 0 in DIFF(dgs) then
%p true;
%p else
%p false;
%p end if;
%p end proc:
%p for n from 1 to 300 do
%p if isA297139(n) then
%p printf("%d,",n) ;
%p end if;
%p end do: # _R. J. Mathar_, Jan 18 2018
%t a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
%t b = 7; t = Table[a[n, b], {n, 1, 10*z}];
%t u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &] (* A297137 *)
%t v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &] (* A297138 *)
%t Complement[Range[z], Union[u, v]] (* A297139 *)
%Y Cf. A297137, A297138.
%K nonn,easy,base
%O 1,2
%A _Clark Kimberling_, Jan 15 2018
|
