

A060288


Distinct (nonoverlapping) twin Harshad numbers whose sum is prime.


3



3, 7, 11, 19, 41, 401, 419, 449, 881, 1021, 1259, 1289, 1471, 1601, 1607, 1871, 1999, 2029, 2281, 2549, 2609, 2833, 3041, 3359, 3457, 4001, 4049, 4481, 4801, 5641, 6329, 7499, 7561, 8081, 8849, 8929, 9613, 9619, 10321, 11131, 12401, 12799, 13033
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OFFSET

0,1


COMMENTS

Suggested by Puzzle 129, The Prime Puzzles and Problems Connection


LINKS

Table of n, a(n) for n=0..42.


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=(p1)/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.


PROG

(UBASIC) 20 A=0; 30 inc A; 40 if Ct=2 then Z=(A1)+(A2): if Z=prmdiv(Z) then print A2; "+"; A1; "="; Z; "/"; :inc Pt; 50 if Ct=2 then Ct=1:A=A1; 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

A005349, A060159, A060289 etc.
Sequence in context: A132449 A132453 A033871 * A191245 A282914 A284027
Adjacent sequences: A060285 A060286 A060287 * A060289 A060290 A060291


KEYWORD

easy,nonn,base


AUTHOR

Enoch Haga, Mar 23 2001


STATUS

approved



