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

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

Table of n, a(n) for n=1..49.

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

Crossrefs

Cf. A037274, A118756, A133959, A133961, A133963, A133965, A133967, A133969, A133971, A133973, A133975, A133977, A133979.

Sequence in context: A338270 A140442 A078731 * A133980 A090312 A089782

Adjacent sequences: A133954 A133955 A133956 * A133958 A133959 A133960

Keyword

nonn,base

Author

Robert G. Wilson v, Sep 30 2007

Extensions

Entry revised by N. J. A. Sloane, Mar 24 2021

Status

approved