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%I #11 Mar 23 2021 15:42:47
%S 211,223,311,337,373,389,547,571,1123,1153,1319,1931,2237,2311,2341,
%T 2371,2557,2719,2797,2953,2971,3167,3181,3191,3257,3313,3329,3347,
%U 3449,3457,3461,3463,3517,3541,3547,3557,3571,3643,3701,3709,3727,3733,3739
%N Home primes whose homeliness is 3.
%C Number of terms < 10^n: 0, 0, 8, 65, 437, 3233, 24579, ... .
%e Only {4, 22, 211} -> 211, etc.
%t 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}];
%t d = 3 - 2; lsu = {}; Do[ If[ lst[[n]] == lst[[n + d]] && lst[[n - 1]] != lst[[n]] && lst[[n]] != lst[[n + d + 1]], AppendTo[lsu, lst[[n]]]], {n, 188004 - d - 1}]; Take[Union@ lsu, 45]
%Y Cf. A037274, A118756, A133959, A133956, A133957, A133958, A133962, A133964, A133966, A133968, A133970, A133972, A133974, A133976, A133978.
%K nonn,base
%O 1,1
%A _Robert G. Wilson v_, Sep 30 2007
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