A001613 -id:A001613 - cp's OEIS frontend

A090730 a(n) = 22*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 22.

2, 22, 482, 10582, 232322, 5100502, 111978722, 2458431382, 53973511682, 1184958825622, 26015120652002, 571147695518422, 12539234180753282, 275292004281053782, 6043884860002429922, 132690174915772404502

Offset: 0

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 18 2004

Indranil Ghosh, Table of n, a(n) for n = 0..743
Tanya Khovanova, Recursive Sequences
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
Index entries for linear recurrences with constant coefficients, signature (22,-1).

Cf. A008951, A016005, A001613, A077422.

a[0] = 2; a[1] = 22; a[n_] := 22a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (* Robert G. Wilson v, Jan 30 2004 *)
LinearRecurrence[{22,-1},{2,22},20] (* Harvey P. Dale, Mar 07 2018 *)

[lucas_number2(n,22,1) for n in range(0,20)] # Zerinvary Lajos, Jun 26 2008

a(n) = p^n + q^n, where p = 11 + 2*sqrt(30) and q = 11 - 2*sqrt(30). - Tanya Khovanova, Feb 06 2007
G.f.: (2-22*x)/(1-22*x+x^2). - Philippe Deléham, Nov 18 2008
a(n) = 2*A077422(n). - R. J. Mathar, Sep 27 2014

A351744 Increment all even digits of n.

Original entry on oeis.org

1, 1, 3, 3, 5, 5, 7, 7, 9, 9, 11, 11, 13, 13, 15, 15, 17, 17, 19, 19, 31, 31, 33, 33, 35, 35, 37, 37, 39, 39, 31, 31, 33, 33, 35, 35, 37, 37, 39, 39, 51, 51, 53, 53, 55, 55, 57, 57, 59, 59, 51, 51, 53, 53, 55, 55, 57, 57, 59, 59, 71, 71, 73, 73, 75, 75, 77, 77

Offset: 0

Alex Ratushnyak, Feb 17 2022

Cf. A001613, A306436, A106747.

Array[FromDigits@ Map[If[EvenQ[#], # + 1, #] &, IntegerDigits[#]] &, 78, 0] (* Michael De Vlieger, Feb 17 2022 *)

a(n) = if (n, fromdigits(apply(x->if(!(x%2),x+1,x), digits(n))), 1); \\ Michel Marcus, Feb 18 2022

for n in range(1000):
  s = str(n)
  res = ''
  for d in s:
    if (int(d) & 1)==0:  d = str(int(d)+1)
    res += d
  print(int(res), end=',')

def A351744(n): return int(str(n).translate({48:49,50:51,52:53,54:55,56:57})) # Chai Wah Wu, Apr 07 2022

cp's OEIS Frontend

A090730 a(n) = 22*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 22.

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