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

1,1

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

Links

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

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)

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A286094 A348187 A098955 * A124885 A115745 A129639

Adjacent sequences: A285467 A285468 A285469 * A285471 A285472 A285473

Keyword

nonn,base,easy

Author

Jamie Robert Creasey, Apr 19 2017

Status

approved