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, 2, 4, 6, 12, 16, 22, 28, 36, 52, 58, 66, 82, 112, 136, 166, 256, 352, 556, 562, 586, 616, 652, 658

Offset: 0

Author

Amarnath Murthy, Nov 10 2003

Keywords

• base
• more
• nonn

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

Examples

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

Crossrefs

Cf. A089695.

Programs

Maple

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=choose([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

Extensions

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