A060290 Primes which are sums of twin Harshad numbers (includes overlaps).

3, 5, 7, 11, 13, 17, 19, 41, 223, 401, 419, 449, 881, 1021, 1259, 1289, 1471, 1601, 1607, 1871, 1999, 2029, 2281, 2549, 2609, 2833, 3041, 3359, 3457, 4001, 4049, 4481, 4801, 4931, 5641, 6329, 7499, 7561, 8081, 8849, 8929, 9613, 9619, 10111, 10321

Offset: 1

Author

Enoch Haga, Mar 24 2001

Keywords

• easy
• nonn
• base

Examples

			a(5)=17, a prime because the first Harshad number is 8 and the second is 9 and 8+9=17. In this sequence overlapping Harshad's are permitted: 1+2=3 and 2+3=5.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005349, A060159, A060288, A060289, A060291.

Programs

Maple

isA005349 := proc(n)
    if n mod digsum(n) = 0 then
        true;
    else
        false;
    end if;
end proc:
isA060290 := proc(n)
    local h1 ;
    if isprime(n) then
        h1 := (n-1)/2 ;
        if isA005349(h1) and isA005349(h1+1) then
            true;
        else
            false;
        end if;
    else
        false;
    end if;
end proc:
for n from 3 to 20000 do
    if isA060290(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Dec 20 2013

Mathematica

harshadQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; s = {}; q1 = True; Do[q2 = harshadQ[n]; If[q1 && q2 && PrimeQ[2*n - 1], AppendTo[s, 2*n - 1]]; q1 = q2, {n, 2, 5000}]; s (* Amiram Eldar, Jan 19 2021 *)

UBASIC

20 A=0;
30 inc A;
40 if Ct=2 then Z=(A-1)+(A-2): if Z=prmdiv(Z) then print A-2; "+"; A-1; "="; Z; "/"; :inc Pt;
50 if Ct=2 then Ct=1:A=A-2;
60 X=1;
70 B=str(A);
80 L=len(B);
90 inc X;
100 S=mid(B,X,1);
110 V=val(S):W=W+V;
120 if XDt+1 then Ct=0:Dt=0;
150 Dt=Ct:W=0;
160 if A<=10 then 30;
170 print Pt;

Formula

{n in A000040: (n-1)/2 in A005349 and (n+1)/2 in A005349}. - R. J. Mathar, Dec 20 2013

Extensions

Offset corrected by Amiram Eldar, Jan 19 2021