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

%I A060290 #21 Jan 19 2021 03:58:29
%S A060290 3,5,7,11,13,17,19,41,223,401,419,449,881,1021,1259,1289,1471,1601,
%T A060290 1607,1871,1999,2029,2281,2549,2609,2833,3041,3359,3457,4001,4049,
%U A060290 4481,4801,4931,5641,6329,7499,7561,8081,8849,8929,9613,9619,10111,10321
%N A060290 Primes which are sums of twin Harshad numbers (includes overlaps).
%H A060290 Amiram Eldar, <a href="/A060290/b060290.txt">Table of n, a(n) for n = 1..10000</a>
%F A060290 {n in A000040:  (n-1)/2 in A005349 and (n+1)/2 in A005349}. - _R. J. Mathar_, Dec 20 2013
%e A060290 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.
%p A060290 isA005349 := proc(n)
%p A060290     if n mod digsum(n) = 0 then
%p A060290         true;
%p A060290     else
%p A060290         false;
%p A060290     end if;
%p A060290 end proc:
%p A060290 isA060290 := proc(n)
%p A060290     local h1 ;
%p A060290     if isprime(n) then
%p A060290         h1 := (n-1)/2 ;
%p A060290         if isA005349(h1) and isA005349(h1+1) then
%p A060290             true;
%p A060290         else
%p A060290             false;
%p A060290         end if;
%p A060290     else
%p A060290         false;
%p A060290     end if;
%p A060290 end proc:
%p A060290 for n from 3 to 20000 do
%p A060290     if isA060290(n) then
%p A060290         printf("%d,",n) ;
%p A060290     end if;
%p A060290 end do: # _R. J. Mathar_, Dec 20 2013
%t A060290 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 *)
%o A060290 (UBASIC)
%o A060290 20 A=0;
%o A060290 30 inc A;
%o A060290 40 if Ct=2 then Z=(A-1)+(A-2): if Z=prmdiv(Z) then print A-2; "+"; A-1; "="; Z; "/"; :inc Pt;
%o A060290 50 if Ct=2 then Ct=1:A=A-2;
%o A060290 60 X=1;
%o A060290 70 B=str(A);
%o A060290 80 L=len(B);
%o A060290 90 inc X;
%o A060290 100 S=mid(B,X,1);
%o A060290 110 V=val(S):W=W+V;
%o A060290 120 if X<L then 90;
%o A060290 130 D=A/W:E=A\W: if D=E then inc Ct;
%o A060290 140 if Ct<>Dt+1 then Ct=0:Dt=0;
%o A060290 150 Dt=Ct:W=0;
%o A060290 160 if A<=10 then 30;
%o A060290 170 print Pt;
%Y A060290 Cf. A005349, A060159, A060288, A060289, A060291.
%K A060290 easy,nonn,base
%O A060290 1,1
%A A060290 _Enoch Haga_, Mar 24 2001
%E A060290 Offset corrected by _Amiram Eldar_, Jan 19 2021