A045798 Oddish numbers (prime to 10 and 10's digit is odd).

11, 13, 17, 19, 31, 33, 37, 39, 51, 53, 57, 59, 71, 73, 77, 79, 91, 93, 97, 99, 111, 113, 117, 119, 131, 133, 137, 139, 151, 153, 157, 159, 171, 173, 177, 179, 191, 193, 197, 199, 211, 213, 217, 219, 231, 233, 237, 239, 251, 253, 257, 259

Offset: 1

Author

J. H. Conway

Keywords

• nonn
• base
• easy
• nice

Comments

From Jianing Song, Apr 27 2019: (Start)

Numbers congruent to {11, 13, 17, 19} mod 20.

Numbers k such that Kronecker(-20,k) = A289741(k) = -1. (End)

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 1, -1).

Crossrefs

Complement of A045797 with respect to A045572.

Programs

Haskell

a045798 n = a045798_list !! (n-1)
a045798_list = filter (odd . (`mod` 10) . (`div` 10)) a045572_list
-- Reinhard Zumkeller, Dec 10 2011

Maple

seq(seq(20*j + k, k = [11, 13, 17, 19]),j=0..100); # Robert Israel, Mar 27 2017

Mathematica

Table[10n+{1,3,7,9},{n,1,31,2}]//Flatten (* Harvey P. Dale, Oct 01 2019 *)

PARI

is(n)=gcd(n,10)==1 && n\10%2 \\ Charles R Greathouse IV, Feb 07 2017

Formula

Conjecture a(n) = a(n-1)+a(n-4)-a(n-5). G.f.: x*(11+2*x+4*x^2+2*x^3+x^4)/((1-x)^2*(1+x)*(1+x^2)). - Colin Barker, Apr 14 2012

a(n) = 5n + O(1). - Charles R Greathouse IV, Feb 07 2017

a(n+4) = a(n) + 20. This confirms Barker's conjecture. - Robert Israel, Mar 27 2017

Extensions

More terms from Erich Friedman.