A319678 - OEIS

%I #29 Jan 20 2021 10:20:16

%S 1,20,21,22,23,24,25,26,27,28,29,300,301,302,303,304,305,306,307,308,

%T 309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,

%U 326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350

%N Numbers with property that the first digit is the length of the number (written in base 10).

%C The last term of this sequence is a(111111111) = 999999999.

%C Numbers n such that A000030(n) = A055642(n). - _Felix Fröhlich_, Sep 27 2018

%H Muniru A Asiru, <a href="/A319678/b319678.txt">Table of n, a(n) for n = 1..1111</a>

%e 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.

%t Select[Range[1000], IntegerDigits[#][[1]] == Length[IntegerDigits[#]] &] (* _Alonso del Arte_, Dec 24 2018 *)

%o (GAP) P:=List([1..340],ListOfDigits);;

%o a:=Filtered([1..Length(P)],i->P[i][1]=Size(P[i])); # _Muniru A Asiru_, Sep 26 2018

%o (PARI) is(n) = #digits(n)==digits(n)[1] \\ _Felix Fröhlich_, Sep 27 2018

%o (PARI) 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

%o (Python)

%o def ok(n): strn = str(n); return int(strn[0]) == len(strn)

%o def aupto(limit): return [m for m in range(1, limit+1) if ok(m)]

%o print(aupto(350)) # _Michael S. Branicky_, Jan 20 2021

%Y Cf. A000030, A055642, A098955.

%K base,easy,nonn,fini

%O 1,2

%A _Halfdan Skjerning_, Sep 26 2018