A195896 Numbers of the form 2*p-1 or 3*p-1 where p is 1 or a prime.

1, 2, 3, 5, 8, 9, 13, 14, 20, 21, 25, 32, 33, 37, 38, 45, 50, 56, 57, 61, 68, 73, 81, 85, 86, 92, 93, 105, 110, 117, 121, 122, 128, 133, 140, 141, 145, 157, 158, 165, 176, 177, 182, 193, 200, 201, 205, 212, 213, 217, 218, 225, 236, 248, 253, 261, 266, 273, 277, 290, 297, 301, 302, 308

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 24 2011

Keywords

• nonn

Examples

			a(1)=1 because p=1 and 2*1 - 1 = 1;
a(2)=2 because p=1 and 3*1 - 1 = 2;
a(3)=3 because p=2 and 2*2 - 1 = 3;
a(4)=5 because p=2 and 3*3 - 1 = 5 or p=3 and p=2 and 3*2 - 1 = 5;
a(5)=8 because p=3 and 3*3 - 1 = 8.
		

Crossrefs

Cf. A196127, A008578.

Programs

Maple

isA195896 := proc(n)
        for p in {(n+1)/2,(n+1)/3} do
        if type(p,'integer') then
                if isprime(p) or p = 1 then
                        return true;
                end if;
        end if;
        end do;
        false ;
end proc:
for n from 1 to 400 do
        if isA195896(n) then
                printf("%d,",n) ;
        end if;
end do: # R. J. Mathar, Oct 15 2011

Mathematica

Union[Flatten[Join[{1,2},{2#-1,3#-1}&/@Prime[Range[50]]]]] (* Harvey P. Dale, Mar 27 2015 *)

Formula

Union of A076274 and A112773.