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A060288 Distinct (non-overlapping) twin Harshad numbers whose sum is prime.

%I A060288 #18 Jan 19 2021 05:49:01
%S A060288 3,7,11,19,41,401,419,449,881,1021,1259,1289,1471,1601,1607,1871,1999,
%T A060288 2029,2281,2549,2609,2833,3041,3359,3457,4001,4049,4481,4801,5641,
%U A060288 6329,7499,7561,8081,8849,8929,9613,9619,10321,11131,12401,12799,13033
%N A060288 Distinct (non-overlapping) twin Harshad numbers whose sum is prime.
%C A060288 Suggested by Puzzle 129, The Prime Puzzles and Problems Connection.
%H A060288 Amiram Eldar, <a href="/A060288/b060288.txt">Table of n, a(n) for n = 1..10000</a>
%H A060288 Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_129.htm">Puzzle 129. Earliest sets of K consecutive Harshad Numbers</a>, The Prime Puzzles and Problems Connection.
%e A060288 a(3)=19, a prime, because the first Harshad number is 9 and the second is 10 and 9+10=19. To find the Harshad numbers take H1=(p-1)/2 as the first Harshad and then the second Harshad, H2=H1+1. Harshad numbers are those which have integral quotients after division by the sum of their digits. Note that 2+3=5 is not included because 1+2=3 are the first twins whose sum is prime and the next twins, 3+4=7, must not overlap the preceding pair.
%t A060288 harshadQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; s = {}; q1 = True; Do[q2 = harshadQ[n]; If[q1 && q2, If[PrimeQ[2*n - 1], AppendTo[s, 2*n - 1]]; q1 = False, q1 = q2], {n, 2, 5000}]; s (* _Amiram Eldar_, Jan 19 2021 *)
%o A060288 (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-1; 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 X<L then 90; 130 D=A/W:E=A\W: if D=E then inc Ct; 140 if Ct<>Dt+1 then Ct=0:Dt=0; 150 Dt=Ct:W=0; 160 if A<10000001 then 30; 170 print Pt;
%Y A060288 Cf. A005349, A060159, A060289, A060290, A060291.
%K A060288 easy,nonn,base
%O A060288 1,1
%A A060288 _Enoch Haga_, Mar 23 2001
%E A060288 Offset corrected by _Amiram Eldar_, Jan 19 2021