Search: id:A089395
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%I A089395
%S A089395 1,2,4,6,12,16,22,28,36,52,58,66,82,106,112,136,166,178,256,306,336,352,
%T A089395 448,502,508,556,562,586,616,652,658,718,982,1018,1108,1162,1192,1228,
%U A089395 1498,1708,2002,2026,2086,2686,2776,2998,3136,3412,3526,3592,4078,4918
%N A089395 Prime productive numbers n: Let the digits of n be abcd. Then the numbers 
               bcd*a+1, cd*ab+1, d*abc+1, abcd+1 etc. are all primes. If n is a 
               k-digit number it produces k such primes.
%C A089395 Conjecture: Sequence is infinite.
%e A089395 256 is a member as 2*56 +1 = 113, 25*6 +1 = 151 and 256+1 = 257 are all 
               primes.
%p A089395 with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j-1),j=1..nops(s))):end: 
               for d from 1 to 6 do sch:=[seq([1,op(i),d+1],i=[[],seq([j],j=2..d)])]: 
               for n from 10^(d-1) to 10^d-1 do sn:=convert(n,base,10): fl:=0: for 
               s in sch do m:=mul(j,j=[seq(ds(sn[s[i]..s[i+1]-1]),i=1..nops(s)-1)])+1: 
               if not isprime(m) then fl:=1: break fi od: if fl=0 then printf("%d, 
               ",n) fi od od: (C. Ronaldo)
%Y A089395 Cf. A089392, A089393, A089394, A089396, A089397.
%Y A089395 Sequence in context: A019280 A090748 A032465 this_sequence A089699 A089696 
               A099316
%Y A089395 Adjacent sequences: A089392 A089393 A089394 this_sequence A089396 A089397 
               A089398
%K A089395 base,nonn
%O A089395 0,2
%A A089395 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 10 2003
%E A089395 Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 
               25 2004

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