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Search: id:A069154
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| A069154 |
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Treated as strings, the concatenation c of the prime factors of n, in increasing order, is an initial segment of n. Equivalently, n begins with c. |
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+0
1
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| 250, 256, 2048, 2176, 2304, 2500, 2560, 2744, 23328, 25000, 25600, 119911, 219488, 236196, 250000, 256000, 262144, 290912, 2097152, 2238728, 2239488, 2317312, 2359296, 2370816, 2500000, 2560000, 3359232, 3515625, 3720087, 5117695
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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All terms listed above have at most three prime factors. Is there an upper bound to the number of prime factors of terms of this sequence?
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EXAMPLE
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The prime factors of 119911 are 11 and 991, which when concatenated yield 11991, an initial segment of 119911. Therefore 119911 is a term of the sequence.
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MATHEMATICA
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g[n_] := Map[ToString, (Transpose[FactorInteger[n]])[[1]]]; h[n_] := Module[{p, l, s, i}, p = g[n]; l = Length[p]; s = p[[1]]; Do[s = s <> p[[k]], {k, 2, l}]; s]; f[n_] := (StringPosition[ToString[n], h[n]] != {}); f2[n_] := f[n] && (StringPosition[ToString[n], g[n]])[[1]][[1]] == 1; Do[If[ ! PrimeQ[n] && f2[n], Print[n]], {n, 2, 10^7}]
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CROSSREFS
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Sequence in context: A033555 A030650 A045254 this_sequence A045169 A045185 A122270
Adjacent sequences: A069151 A069152 A069153 this_sequence A069155 A069156 A069157
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KEYWORD
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base,nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Apr 08 2002
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