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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 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.)