A285470 - OEIS

%I #38 Dec 22 2021 07:03:19

%S 12,22,32,42,52,62,72,82,92,120,121,122,123,124,125,126,127,128,129,

%T 220,221,222,223,224,225,226,227,228,229,320,321,322,323,324,325,326,

%U 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

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

%C 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

%H David A. Corneth, <a href="/A285470/b285470.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Robert Israel_, Jun 12 2017: (Start)

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

%F 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)

%e a(21) = 221, a(36) = 326.

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

%p 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

%t Table[FromDigits@ Apply[Join, {{First@ #}, {2}, Rest@ #}] &@ IntegerDigits@ n, {n, 67}] (* _Michael De Vlieger_, Jun 12 2017 *)

%o (PARI) isok(n) = (n>9) && digits(n)[2] == 2; \\ _Michel Marcus_, Jun 12 2017

%o (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

%o (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

%o (Python)

%o def a(n): s = str(n); return int(s[0] + "2" + s[1:])

%o print([a(n) for n in range(1, 68)]) # _Michael S. Branicky_, Dec 22 2021

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

%K nonn,base,easy

%O 1,1

%A _Jamie Robert Creasey_, Apr 19 2017