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

Offset: 1

Author

Halfdan Skjerning, Sep 26 2018

Keywords

• base
• easy
• nonn
• fini

Comments

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

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000030, A055642, A098955.

Programs

GAP

P:=List([1..340],ListOfDigits);;
a:=Filtered([1..Length(P)],i->P[i][1]=Size(P[i])); # Muniru A Asiru, Sep 26 2018

Mathematica

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