

A089696


Numbers k such that the numbers obtained by placing as many '*' signs as possible anywhere between the digits and then adding 1 yields a prime in every case: let abc.. be the digits of k, then abc+1, a*bc+1, ab*c+1, a*b*c+1, ... must all be primes.


1



1, 2, 4, 6, 12, 16, 22, 28, 36, 52, 58, 66, 82, 112, 136, 166, 256, 352, 556, 562, 586, 616, 652, 658
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Though the first 14 terms match with that of A089395, the next term of A089395 306 is not a member of this sequence. Conjecture: Sequence is finite.
No more terms < 10^7. The first 13 terms match with that of A089395, but A089395(14) = 106 is not included because 1*0*6+1 = 1 is not prime.  David Wasserman, Oct 04 2005


LINKS



EXAMPLE

256 is a member 256+1, 2*56 +1, 25*6+1, 2*5*6 +1 are all prime.


MAPLE

with(combinat): ds:=proc(s) local j: RETURN(add(s[j]*10^(j1), j=1..nops(s))):end: for d from 1 to 6 do sch:=[seq([1, op(i), d+1], i=choose([seq(j, j=2..d)]))]: for n from 10^(d1) to 10^d1 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


CROSSREFS



KEYWORD

base,more,nonn


AUTHOR



EXTENSIONS

Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004


STATUS

approved



