A088265 Numbers of the form 10^k + 1, 3, 7, or 9 for k>=1.

11, 13, 17, 19, 101, 103, 107, 109, 1001, 1003, 1007, 1009, 10001, 10003, 10007, 10009, 100001, 100003, 100007, 100009, 1000001, 1000003, 1000007, 1000009, 10000001, 10000003, 10000007, 10000009, 100000001, 100000003, 100000007, 100000009, 1000000001, 1000000003, 1000000007, 1000000009

Offset: 1

Author

Amarnath Murthy, Sep 28 2003

Keywords

• base
• nonn
• easy

Comments

A 10-automatic sequence: terms match the regular expression 10*[1379]. - Charles R Greathouse IV, Oct 15 2012

Primes in the sequence are at positions 1 to 8, 12, 15, 16, 18, 22, 31, 35, 36, 42, 66, 70, 72, 88, 95,... R. J. Mathar, Oct 16 2012

Links

• Index entries for 10-automatic sequences.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,11,0,0,0,-10).

Crossrefs

Cf. A088266, A000533.

Programs

Maple

A088265 := proc(n)
    if n <=8 then
        op(n,[11,13,17,19,101,103,107,109]) ;
    else
        11*procname(n-4)-10*procname(n-8) ;
    end if;
end proc: # R. J. Mathar, Oct 16 2012

Mathematica

Flatten @ Table[10^n + m, {n, 50}, {m, {1, 3, 7, 9}}] (* Mikk Heidemaa, Mar 06 2020 *)

PARI

A088265(n)=10^((n+3)\4)+[9,1,3,7][n%4+1]  \\ M. F. Hasler, Oct 15 2012

Formula

a(4n+r) = 10^(n+1) + k, (r, k) = (1, 1), (2, 3), (3, 7) or (4, 9).

G.f. -x*(-11-13*x-17*x^2-19*x^3+20*x^4+40*x^5+80*x^6+100*x^7) / ( (x-1)*(1+x)*(1+x^2)*(10*x^4-1) ). a(n)= 11*a(n-4) -10*a(n-8). - R. J. Mathar, Oct 16 2012

Extensions

More terms from Max Alekseyev, Oct 14 2012