login
A133957
Form the list of home primes A037274(c) for c composite, and sort into increasing order.
24
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
OFFSET
1,1
COMMENTS
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
LINKS
Patrick De Geest, Home Primes < 100 and Beyond.
Eric Weisstein's World of Mathematics, Home Prime.
EXAMPLE
The home primes corresponding to the first few composite numbers c are as follows:
c A037274(c)
4 211
6 23
8 3331113965338635107
9 311
10 773
12 223
14 13367
15 1129
16 31636373
18 233
20 3318308475676071413
21 37
... ...
MATHEMATICA
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
KEYWORD
nonn,base
AUTHOR
Robert G. Wilson v, Sep 30 2007
EXTENSIONS
Entry revised by N. J. A. Sloane, Mar 24 2021
STATUS
approved