OFFSET
1,1
COMMENTS
Suggested by Puzzle 129, The Prime Puzzles and Problems Connection.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Carlos Rivera, Puzzle 129. Earliest sets of K consecutive Harshad Numbers, The Prime Puzzles and Problems Connection.
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(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;
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Enoch Haga, Mar 23 2001
EXTENSIONS
Offset corrected by Amiram Eldar, Jan 19 2021
STATUS
approved