This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Select[Range[90],FreeQ[Differences[IntegerDigits[#,5]],0]&] (* Harvey P. Dale, Nov 30 2019 *)
Select[Range[0,200],FreeQ[Differences[IntegerDigits[#,3]],0]&] (* Harvey P. Dale, Feb 25 2022 *)
a(n, base=3) = { for (b=0, oo, if (n <= (base-1)*2^b, my (v=ceil(n/2^b), p=(n-1)%(2^b)); while (b>0, v=base*v+vecsort([(v-1)%base, (v+1)%base])[1+bittest(p,b--)];); return (v), n -= (base-1)*2^b);); } \\ Rémy Sigrist, Sep 15 2022
mRunLen := proc(L)
if nops(L) = 0 then
0;
else
a := 1 ;
for i from 2 to nops(L) do
if op(i,L) = op(i-1,L) then
a := a+1 ;
else
a := max(a, procname([op(i..nops(L),L)])) ;
break;
end if;
end do:
a ;
end if ;
end proc:
A043277 := proc(n)
convert(n,base,3) ;
mRunLen(%) ;
end proc:
seq(A043277(n),n=1..100) ; # R. J. Mathar, Jul 26 2015
Table[Max[Length/@Split[IntegerDigits[n,3]]],{n,90}] (* Harvey P. Dale, Aug 24 2019 *)
A043277(n, b=3)={my(m,c=1); while(n>0, n%b==(n\=b)%b && c++ && next; m=max(m, c); c=1); m} \\ - M. F. Hasler, Jul 23 2013
Select[Range[0,80],FreeQ[Differences[IntegerDigits[#,6]],0]&] (* Harvey P. Dale, Sep 09 2016 *)
isA043095 := proc(n) dgs := convert(n,base,9) ; for i from 2 to nops(dgs) do if op(i,dgs) = op(i-1,dgs) then return false; end if; end do: true ; end proc: A043095 := proc(n) option remember; if n =1 then 0; else for a from procname(n-1)+1 do if isA043095(a) then return a; end if; end do; end if; end proc: seq(A043095(n),n=1..120) ; # R. J. Mathar, Dec 28 2023
Select[Range[0,100],!MemberQ[Flatten[Differences/@Partition[ IntegerDigits[ #,9],2,1]],0]&] (* Harvey P. Dale, Apr 05 2014 *)
isok(n) = {my(d = digits(n, 9)); for (i=2, #d, if (d[i] == d[i-1], return (0));); return (1);} \\ Michel Marcus, Oct 11 2017
The first terms, alongside their balanced ternary expansions, are: n a(n) bter(a(n)) -- ---- ---------- 1 0 0 2 1 1 3 2 1T 4 3 10 5 6 1T0 6 7 1T1 7 8 10T 8 10 101 9 17 1T0T 10 19 1T01 11 20 1T1T 12 21 1T10 13 24 10T0 14 25 10T1 15 29 101T 16 30 1010
is(n) = { while (n, my (d = centerlift(Mod(n, 3))); n = (n-d)/3; if (d==centerlift(Mod(n, 3)), return (0););); return (1); }
a(n) = { my (d = binary(n)); for (i = 2, #d, d[i] = setminus([-1,0,1], [d[i-1]])[1+d[i]];); fromdigits(d, 3); }
Select[Range[0,80],FreeQ[Differences[IntegerDigits[#,8]],0]&] (* Harvey P. Dale, Nov 08 2022 *)
10 is 1010 in base 2 and 101 in base 3; no two of the same digit are next to one another and so 10 is a term. Similarly 21 is 10101 in base 2 and 210 in base 3 so it is also a term.
isokd(d) = {dd = vector(#d-1, k, abs(d[k+1]-d[k])); if (#dd, vecmin(dd), 1);}
isok(n) = isokd(binary(n)) && isokd(digits(n, 3)); \\ Michel Marcus, Oct 14 2015
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