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Search: id:A089696
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| A089696 |
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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. |
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+0
2
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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 (wasserma(AT)spawar.navy.mil), Oct 04 2005
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EXAMPLE
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256 is a member 256+1, 2*56 +1, 25*6+1, 2*5*6 +1 are all prime.
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MAPLE
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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)
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CROSSREFS
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Cf. A089695.
Sequence in context: A032465 A089395 A089699 this_sequence A099316 A007416 A098895
Adjacent sequences: A089693 A089694 A089695 this_sequence A089697 A089698 A089699
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KEYWORD
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base,more,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 10 2003
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EXTENSIONS
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Corrected and extended by C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 25 2004
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