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A133957
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Form the list of home primes A037274(c) for c composite, and sort into increasing order.
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24
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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
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OFFSET
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1,1
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COMMENTS
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The old name was "Home primes the result of composite numbers."
Number of terms < 10^n: 0, 2, 37, 274, 2087, 15472, 123261, ....
Increasing sequence of all prime numbers which are concatenations of at least two primes ordered in nondecreasing order (e.g., 227=2.2.7, 1319=13.19). - Bartlomiej Pawlik, Aug 06 2023
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LINKS
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Eric Weisstein's World of Mathematics, Home Prime.
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EXAMPLE
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The home primes corresponding to the first few composite numbers c are as follows:
4 211
6 23
8 3331113965338635107
9 311
10 773
12 223
14 13367
15 1129
16 31636373
18 233
20 3318308475676071413
21 37
... ...
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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.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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