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.
Halfdan Skjerning's wiki page.
Halfdan Skjerning has authored 32 sequences. Here are the ten most recent ones:
300 belongs to the sequence since its initial digit is 3 and the number has three digits. 3001 does not belong to the sequence since its initial digit is 3, but the number has four digits in total.
P:=List([1..340],ListOfDigits);; a:=Filtered([1..Length(P)],i->P[i][1]=Size(P[i])); # Muniru A Asiru, Sep 26 2018
Select[Range[1000], IntegerDigits[#][[1]] == Length[IntegerDigits[#]] &] (* Alonso del Arte, Dec 24 2018 *)
is(n) = #digits(n)==digits(n)[1] \\ Felix Fröhlich, Sep 27 2018
a(n,base=10) = for (w=1, oo, my (c=base^(w-#digits(w,base))); if (n<=c, return (c*w+n-1), n-=c)) \\ Rémy Sigrist, Dec 25 2018
def ok(n): strn = str(n); return int(strn[0]) == len(strn) def aupto(limit): return [m for m in range(1, limit+1) if ok(m)] print(aupto(350)) # Michael S. Branicky, Jan 20 2021
11 and 111 belong to the set as they both have the same number of digits as their digital root, respectively; 11 has two digits and also digital root two, and 111 has three digits and digital root three. 302563 does not belong to the set, since it has six digits and digital root one.
Select[Range[1000], IntegerLength[#] == Mod[#-1, 9] + 1 &] (* Giovanni Resta, Aug 16 2018 *)
isok(n) = if(n, (n-1)%9+1) == #Str(n); \\ Michel Marcus, Aug 16 2018
PadRight[{},120,{1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8}] (* Harvey P. Dale, Feb 10 2024 *)
Vec(x*(1 + 9*x + 11*x^2 + 9*x^3 + 11*x^4 + 9*x^5 + 11*x^6 + 9*x^7 + 11*x^8 + 8*x^9) / ((1 - x)*(1 + x)*(1 + x + x^2)*(1 + x^3 + x^6)) + O(x^50)) \\ Colin Barker, May 28 2018
LinearRecurrence[{0,1,0,0,0,0,0,-1,0,1},{1,8,3,6,5,4,7,2,9,0},100] (* or *) PadRight[{},100,{1,8,3,6,5,4,7,2,9,0,7,2,5,4,3,6}] (* Harvey P. Dale, Sep 28 2021 *)
Vec(x*(1 + 8*x + 2*x^2 - 2*x^3 + 2*x^4 - 2*x^5 + 2*x^6 - 2*x^7 + 3*x^8 + 6*x^9) / ((1 - x)*(1 + x)*(1 + x^8)) + O(x^50)) \\ Colin Barker, May 28 2018
909 has more 9's than any other digit, whereas both 9009 and 9019 have as many other digits as 9's.
Select[Range[0, 10^4], Total@ #1 < First@ #2 & @@ TakeDrop[RotateLeft[#, 9] &@ DigitCount@ #, 9] &] (* Michael De Vlieger, Sep 25 2017 *) Select[Range[10000],2*DigitCount[#,10, 9]>IntegerLength[#]&] (* Harvey P. Dale, Aug 04 2019 *)
808 has more 8's than any other digit, whereas both 8008 and 8018 have as many other digits as 8's.
Select[Range[0, 9000], Total@ #1 < First@ #2 & @@ TakeDrop[RotateLeft[#, 8] &@ DigitCount@ #, 9] &] (* Michael De Vlieger, Sep 25 2017 *)
707 has more 7's than any other digit, whereas both 7007 and 7017 have as many other digits as 7's.
Select[Range[0, 8000], Total@ #1 < First@ #2 & @@ TakeDrop[RotateLeft[#, 7] &@ DigitCount@ #, 9] &] (* Michael De Vlieger, Sep 25 2017 *)
606 has more 6's than any other digit, whereas both 6006 and 6016 have as many other digits as 6's.
F:= proc(d) local s, m, T;
s:= 6*(10^d-1)/9;
T:= select(`>=`,{seq(seq(seq(s+G(c,k), k = 0 .. 10^m-1),c = combinat:-choose([$0..d-1],m)),m=0 .. floor((d-1)/2))},10^(d-1));
op(sort(convert(T,list)))
end proc:
G:= proc(c,k) local L,m,j;
m:= nops(c);
L:= convert(10^m+k,base,10);
add((L[j]-6)*10^c[j], j=1..m)
end proc:
seq(F(d),d=1..4); # Robert Israel, Sep 24 2017
Select[Range[0, 6700], Total@ #1 < First@ #2 & @@ TakeDrop[RotateLeft[#, 6] &@ DigitCount@ #, 9] &] (* Michael De Vlieger, Sep 22 2017 *)
505 has more 5's than any other digit, whereas both 5005 and 5015 have as many other digits as 5's.
Select[Range[0, 6000], Total@ #1 < First@ #2 & @@ TakeDrop[RotateLeft[#, 5] &@ DigitCount@ #, 9] &] (* Michael De Vlieger, Sep 22 2017 *) Select[Range[6000],DigitCount[#,10,5]>(IntegerLength[#]-DigitCount[#,10,5])&] (* Harvey P. Dale, May 08 2022 *)
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