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

0,2

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

Table of n, a(n) for n=0..23.

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^(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

Crossrefs

Cf. A089695.

Sequence in context: A032465 A089395 A089699 * A171609 A099316 A007416

Adjacent sequences: A089693 A089694 A089695 * A089697 A089698 A089699

Keyword

base,more,nonn

Author

Amarnath Murthy, Nov 10 2003

Extensions

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

Status

approved