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A297142 Numbers whose base-8 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}. 5

%I

%S 1,2,3,4,5,6,7,9,18,27,36,45,54,63,64,72,73,74,75,76,77,78,79,82,91,

%T 100,109,118,127,128,137,144,145,146,147,148,149,150,151,155,164,173,

%U 182,191,192,201,210,216,217,218,219,220,221,222,223,228,237,246

%N Numbers whose base-8 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 A297140 and A297141.

%C Differs from A044819 first for 513 = 1001_8, which has two consecutive equal digits and is in this sequence, but has two runs of equal length (1), and is not in A044819. - _R. J. Mathar_, Jan 17 2018

%e Base-8 digits of 5000: 1,1,6,1,0, so that 5000 is in the sequence.

%p read("transforms") :

%p isA297142 := proc(n)

%p local dgs,ud;

%p dgs := convert(n,base,8) ;

%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 isA297142(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 = 8; t = Table[a[n, b], {n, 1, 10*z}];

%t u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &] (* A297140 *)

%t v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &] (* A297141 *)

%t Complement[Range[z], Union[u, v]] (* A297142 *)

%Y Cf. A297140, A297142.

%K nonn,easy,base

%O 1,2

%A _Clark Kimberling_, Jan 15 2018

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)