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%I #28 Sep 06 2023 21:11:44
%S 23,37,211,223,227,229,233,241,257,271,277,283,311,313,317,331,337,
%T 347,353,359,367,373,379,383,389,397,523,541,547,557,571,577,719,743,
%U 761,773,797,1117,1123,1129,1153,1171,1319,1361,1367,1373,1723,1741,1747
%N Form the list of home primes A037274(c) for c composite, and sort into increasing order.
%C The old name was "Home primes the result of composite numbers."
%C Number of terms < 10^n: 0, 2, 37, 274, 2087, 15472, 123261, ....
%C 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
%H Patrick De Geest, <a href="http://www.worldofnumbers.com/topic1.htm">Home Primes < 100 and Beyond</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HomePrime.html">Home Prime</a>.
%e The home primes corresponding to the first few composite numbers c are as follows:
%e c A037274(c)
%e 4 211
%e 6 23
%e 8 3331113965338635107
%e 9 311
%e 10 773
%e 12 223
%e 14 13367
%e 15 1129
%e 16 31636373
%e 18 233
%e 20 3318308475676071413
%e 21 37
%e ... ...
%t 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
%Y Cf. A037274, A118756, A133959, A133961, A133963, A133965, A133967, A133969, A133971, A133973, A133975, A133977, A133979.
%K nonn,base
%O 1,1
%A _Robert G. Wilson v_, Sep 30 2007
%E Entry revised by _N. J. A. Sloane_, Mar 24 2021
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