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Search: id:A094043
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| A094043 |
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Alternate composite and prime numbers not included earlier such that every partial concatenation is a prime: a(2n) is prime and a(2n-1) is not prime. |
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+0
2
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| 1, 3, 9, 13, 63, 107, 27, 67, 39, 23, 49, 29, 99, 439, 207, 41, 357, 229, 77, 139, 69, 839, 133, 239, 121, 317, 187, 53, 33, 1291, 177, 557, 171, 1753, 323, 19, 519, 953, 231, 523, 321, 251, 327, 31, 299, 2203, 747, 101, 81, 1741, 291, 6779, 261, 1549, 1463, 97, 297
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture: 2 and 5 are the only two nonmembers.
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EXAMPLE
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1, 13, 139, 13913, 1391363, 1391363107,..., etc. are not composite.
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MATHEMATICA
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p = Prime[ Range[ 1500]]; np = Drop[ Complement[ Range[ 1500], p], 1]; a[1] = 1; a[n_] := a[n] = Block[{k = 1, q = Flatten[ IntegerDigits[ # ] & /@ Table[ a[i], {i, n - 1}]]}, If[ EvenQ[n], While[ !PrimeQ[ FromDigits[ Join[q, IntegerDigits[ p[[k]] ]]]], k++ ]; q = p[[k]]; p = Delete[p, k]; q, While[ !PrimeQ[ FromDigits[ Join[q, IntegerDigits[ np[[k]] ]]]], k++ ]; q = np[[k]]; np = Delete[np, k]; q]]; Table[ a[n], {n, 60}]
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CROSSREFS
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Cf. A088614, A094045.
Sequence in context: A068885 A018292 A089147 this_sequence A134190 A047905 A134904
Adjacent sequences: A094040 A094041 A094042 this_sequence A094044 A094045 A094046
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KEYWORD
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nonn,base
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 23 2004
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