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Search: id:A133957
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| A133957 |
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Home primes the result of composite numbers. |
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+0
15
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| 23, 37, 211, 223, 227, 229, 233, 241, 257, 271, 277, 283, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 389, 397, 523, 541, 547, 557, 571, 577, 719, 743, 761, 773, 797, 1117, 1123, 1129, 1153, 1171, 1319, 1361, 1367, 1373, 1723, 1741, 1747
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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While all primes yield themselves and thus all primes are home primes, this sequence is the result of beginning with composite numbers whose trajectory are the home primes above.
Home primes whose 'homilness' is greater than one.
Number of terms < 10^n: 0, 2, 37, 274, 2087, 15472, 123261, ....
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LINKS
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P. De Geest, Home Primes < 100 and Beyond.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics..
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EXAMPLE
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4 -> 211, 6 -> 23, 8 -> 3331113965338635107.
The trajectory of 9 is as follows: 9 = 3*3 -> 33 = 3*11 -> 311, a prime, so the home prime of 9 is 311.
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MATHEMATICA
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lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 1000}]; Union@ lst
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CROSSREFS
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Cf. A037274, A118756, A133959, A133961, A133963, A133965, A133967, A133969, A133971, A133973, A133975, A133977, A133979.
Sequence in context: A068016 A140442 A078731 this_sequence A133980 A090312 A089782
Adjacent sequences: A133954 A133955 A133956 this_sequence A133958 A133959 A133960
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 30 2007
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