A091628 Concatenation of n 2's followed by 3.

23, 223, 2223, 22223, 222223, 2222223, 22222223, 222222223, 2222222223, 22222222223, 222222222223, 2222222222223, 22222222222223, 222222222222223, 2222222222222223, 22222222222222223, 222222222222222223

Offset: 1

Author

Enoch Haga, Jan 24 2004

Keywords

• base
• easy
• nonn

Comments

Sequence arising in Farideh Firoozbakht's solution to Prime Puzzle 251; 23 is the only pointer prime (A089823) not containing the digit "1".

Links

• Tanya Khovanova, Recursive Sequences
• Carlos Rivera's Prime Puzzles and Problems Connection, Puzzle 251, Pointer primes
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A089823, A091629, A091630, A091631, A091632.

Programs

Magma

[ n eq 1 select 23 else 10*Self(n-1)-7: n in [1..17] ];

Formula

a(n) = (10^(n+1) - 1)/9*2 + 1.

a(n) = 10*a(n-1) - 7, with a(1)=23. - Vincenzo Librandi, Nov 16 2010

From Colin Barker, May 06 2012: (Start)

a(n) = 11*a(n-1) - 10*a(n-2).

G.f.: x*(23-30*x)/((1-x)*(1-10*x)). (End)

Extensions

Edited and extended by Ray Chandler, Feb 07 2004