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A133957 Form the list of home primes A037274(c) for c composite, and sort into increasing order.

%I A133957 #29 Feb 16 2025 08:33:06
%S A133957 23,37,211,223,227,229,233,241,257,271,277,283,311,313,317,331,337,
%T A133957 347,353,359,367,373,379,383,389,397,523,541,547,557,571,577,719,743,
%U A133957 761,773,797,1117,1123,1129,1153,1171,1319,1361,1367,1373,1723,1741,1747
%N A133957 Form the list of home primes A037274(c) for c composite, and sort into increasing order.
%C A133957 The old name was "Home primes the result of composite numbers."
%C A133957 Number of terms < 10^n: 0, 2, 37, 274, 2087, 15472, 123261, ....
%C A133957 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 A133957 Patrick De Geest, <a href="http://www.worldofnumbers.com/topic1.htm">Home Primes < 100 and Beyond</a>.
%H A133957 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HomePrime.html">Home Prime</a>.
%e A133957 The home primes corresponding to the first few composite numbers c are as follows:
%e A133957    c            A037274(c)
%e A133957    4            211
%e A133957    6            23
%e A133957    8            3331113965338635107
%e A133957    9            311
%e A133957    10           773
%e A133957    12           223
%e A133957    14           13367
%e A133957    15           1129
%e A133957    16           31636373
%e A133957    18           233
%e A133957    20           3318308475676071413
%e A133957    21           37
%e A133957    ...          ...
%t A133957 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 A133957 Cf. A037274, A118756, A133959, A133961, A133963, A133965, A133967, A133969, A133971, A133973, A133975, A133977, A133979.
%K A133957 nonn,base
%O A133957 1,1
%A A133957 _Robert G. Wilson v_, Sep 30 2007
%E A133957 Entry revised by _N. J. A. Sloane_, Mar 24 2021