A285470 Numbers k where "2" appears as the second digit of the decimal representation.

12, 22, 32, 42, 52, 62, 72, 82, 92, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 620, 621, 622, 623, 624, 625, 626, 627

Offset: 1

Author

Jamie Robert Creasey, Apr 19 2017

Keywords

• nonn
• base
• easy

Comments

To find a(n), concatenate the first digit of n with 2 and then the other digits (if any) from n. See example. - David A. Corneth, Jun 12 2017

Examples

			a(21) = 221, a(36) = 326.
As the first digit of 983 is 9, and the others are 83, a(983) = 9283. - _David A. Corneth_, Jun 12 2017
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A011532 (containing 2), A052404 (without 2), A217394 (starting with 2).

Programs

Maple

seq(seq(seq(a*10^d + 2*10^(d-1)+c, c=0..10^(d-1)-1),a=1..9),d=1..2); # Robert Israel, Jun 12 2017

Mathematica

Table[FromDigits@ Apply[Join, {{First@ #}, {2}, Rest@ #}] &@ IntegerDigits@ n, {n, 67}] (* Michael De Vlieger, Jun 12 2017 *)
Select[Range[700],NumberDigit[#,IntegerLength[#]-2]==2&] (* Harvey P. Dale, Aug 15 2025 *)

PARI

isok(n) = (n>9) && digits(n)[2] == 2; \\ Michel Marcus, Jun 12 2017

PARI

a(n) = my(d = digits(n)); fromdigits(concat([d[1], [2], vector(#d-1, i, d[i+1])])) \\ David A. Corneth, Jun 12 2017

PARI

nxt(n) = if(isok(n+1), n+1, d = digits(n); t = 9*10^(#d-2); if(d[1]==9,t*=3); n+=t++) \\ David A. Corneth, Jun 12 2017

Python

def a(n): s = str(n); return int(s[0] + "2" + s[1:])
print([a(n) for n in range(1, 68)]) # Michael S. Branicky, Dec 22 2021

Formula

From Robert Israel, Jun 12 2017: (Start)

a(10*n+j) = 10*a(n)+j for 0<=j<=9 and n >= 1.

G.f. g(x) satisfies g(x) = 10*(1-x^10)*g(x^10)/(1-x) + (x + 2*x + ... + 9*x^9)*x^10/(1-x^10) + 12*x + 22*x^2 + ... + 92*x^9. (End)