A095761 a(n) = A014824(2*n-1).

1, 123, 12345, 1234567, 123456789, 12345679011, 1234567901233, 123456790123455, 12345679012345677, 1234567901234567899, 123456790123456790121, 12345679012345679012343

Offset: 1

Author

Michael Joseph Halm, Jul 10 2004

Keywords

• easy
• nonn
• base

Comments

Previous name was: Numbers whose square root shows strings of seemingly rational and irrational strings.

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..101
• K. S. Brown, Schizophrenic numbers

Crossrefs

Cf. A014824.

Programs

GAP

a:=[1];; for n in [2..20] do a[n]:=100*a[n-1]+22*n-21; od; a; # Muniru A Asiru, Mar 30 2018

Magma

[-19/81-(2/9)*(n-1)+(100/81)*100^(n-1): n in [1..20]]; // Vincenzo Librandi, Apr 03 2018

Mathematica

RecurrenceTable[{a[1]==1, a[n]==100 a[n-1] + 22 n - 21}, a, {n, 20}] (* Vincenzo Librandi, Apr 03 2018 *)

PARI

a=vector(10^3); a[1]=1; for(n=2, #a, a[n]=100*a[n-1]+22*n-21); a \\ Altug Alkan, Mar 30 2018

Formula

a(1) = 1; for n > 1, a(n) = 100*a(n - 1) + 22*n - 21.

O.g.f.: x(1+21x)/((-1+x)^2*(1-100x)) = -17/(81(-1+x)) - 1/(81(-1+100*x)) - 2/(9(-1+x)^2). - R. J. Mathar, Feb 01 2008

Extensions

Better name from Georg Fischer, Mar 30 2018