A045797 Evenish numbers (prime to 10 and 10's digit is even).

1, 3, 7, 9, 21, 23, 27, 29, 41, 43, 47, 49, 61, 63, 67, 69, 81, 83, 87, 89, 101, 103, 107, 109, 121, 123, 127, 129, 141, 143, 147, 149, 161, 163, 167, 169, 181, 183, 187, 189, 201, 203, 207, 209, 221, 223, 227, 229, 241, 243, 247, 249, 261, 263, 267, 269, 281

Offset: 1

Author

J. H. Conway

Keywords

• nonn
• base
• easy
• nice

Comments

From Jianing Song, Apr 27 2019: (Start)

Numbers congruent to {1, 3, 7, 9} mod 20.

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

First 20 terms are congruences of 3^k mod 100. - Dario Vuksan, Jan 09 2023

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 A045798 with respect to A045572.

Programs

Haskell

a045797 n = a045797_list !! (n-1)
a045797_list = filter (even . (`mod` 10) . (`div` 10)) a045572_list
-- Reinhard Zumkeller, Dec 10 2011

Mathematica

Flatten[Table[10n+{1,3,7,9},{n,0,30,2}]] (* Harvey P. Dale, Dec 05 2012 *)

PARI

is(n)=gcd(n,10)==1 && n\10%2==0 \\ Charles R Greathouse IV, Sep 24 2015

Formula

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

The conjecture above is correct. - Jianing Song, Apr 27 2019

a(n) = 5n + O(1). - Charles R Greathouse IV, Jan 09 2023

Extensions

More terms from Erich Friedman

Offset changed by Reinhard Zumkeller, Dec 10 2011