A083818 Numbers k such that 2k-1 is the digit reversal of k.

1, 37, 397, 3997, 39997, 399997, 3999997, 39999997, 399999997, 3999999997, 39999999997, 399999999997, 3999999999997, 39999999999997, 399999999999997, 3999999999999997, 39999999999999997, 399999999999999997, 3999999999999999997, 39999999999999999997, 399999999999999999997

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 08 2003

Keywords

• base
• easy
• nonn

Comments

a(n) = 1 + 36 + 360 + 3600 + 36000 + ..., for a total of n terms. a(n) = 1 + sum of first n-1 terms of the geometric progression with first term 36 and common ratio 10. a(n) = 1 + 36*A000042(n-1) (the unary sequence).

Examples

			2*37 - 1 = 73.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A000042, A083811, A083812, A083813.

Digit reversals of A169830.

Programs

PARI

my(x='x+O('x^22)); Vec(x*(1+26*x)/((1-x)*(1-10*x))) \\ Elmo R. Oliveira, Jun 12 2025

Formula

a(n) = 4*10^(n-1) - 3.

From Elmo R. Oliveira, Jun 12 2025: (Start)

G.f.: x*(26*x+1)/((x-1)*(10*x-1)).

E.g.f.: (13 - 15*exp(x) + 2*exp(10*x))/5.

a(n) = 11*a(n-1) - 10*a(n-2) for n >= 3. (End)

Extensions

a(1)=1 inserted by David Radcliffe, Jul 25 2015