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A133957 Home primes the result of composite numbers. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

While all primes yield themselves and thus all primes are home primes, this sequence is the result of beginning with composite numbers whose trajectory are the home primes above.

Home primes whose 'homilness' is greater than one.

Number of terms < 10^n: 0, 2, 37, 274, 2087, 15472, 123261, ....

LINKS

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

P. De Geest, Home Primes < 100 and Beyond.

Eric Weisstein's World of Mathematics, Home Prime..

EXAMPLE

4 -> 211, 6 -> 23, 8 -> 3331113965338635107.

The trajectory of 9 is as follows: 9 = 3*3 -> 33 = 3*11 -> 311, a prime, so the home prime of 9 is 311.

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: A068016 A140442 A078731 * A133980 A090312 A089782

Adjacent sequences:  A133954 A133955 A133956 * A133958 A133959 A133960

KEYWORD

nonn,base

AUTHOR

Robert G. Wilson v, Sep 30 2007

STATUS

approved

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Last modified August 6 15:15 EDT 2020. Contains 336248 sequences. (Running on oeis4.)