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Search: id:A089695
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| A089695 |
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Numbers n such that placing as many possible '+' signs anywhere in between the digits yields a prime in every case. Let abcd... be the digits of n; then abcd, a+bcd, ab+cd, abc+d, a+b+cd, a+bc +d, ab+c+d, a+b+c+d, ... are all prime. |
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+0
2
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| 2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 227, 229, 281, 401, 443, 449, 467, 601, 607, 647, 661, 683, 809, 821, 863, 881, 4001, 4463, 4643, 6007, 6067, 6803, 8009
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Though the first 27 terms match those of A089392, the next term of A089392 (2221) is not a member of this sequence. Conjecture: sequence is finite.
No more terms < 10^8. - David Wasserman (wasserma(AT)spawar.navy.mil), Oct 04 2005
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EXAMPLE
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863 is a member 863, 8+63, 86+3, 8+6+3 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:=add(j, j=[seq(ds(sn[s[i]..s[i+1]-1]), i=1..nops(s)-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. A089696.
Sequence in context: A129945 A046704 A089392 this_sequence A070027 A118723 A118721
Adjacent sequences: A089692 A089693 A089694 this_sequence A089696 A089697 A089698
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KEYWORD
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base,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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