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A060288 Distinct (non-overlapping) 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 (list; graph; refs; listen; history; text; internal format)
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=(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.

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

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

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Last modified June 15 20:50 EDT 2019. Contains 324145 sequences. (Running on oeis4.)