A319678 - OEIS

A319678

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

1, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

Numbers n such that A000030(n) = A055642(n). - Felix Fröhlich, Sep 27 2018

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..1111

EXAMPLE

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.

MATHEMATICA

Select[Range[1000], IntegerDigits[#][[1]] == Length[IntegerDigits[#]] &] (* Alonso del Arte, Dec 24 2018 *)

PROG

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

a:=Filtered([1..Length(P)], i->P[i][1]=Size(P[i])); # Muniru A Asiru, Sep 26 2018

(PARI) is(n) = #digits(n)==digits(n)[1] \\ Felix Fröhlich, Sep 27 2018

(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

(Python)

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

CROSSREFS