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%I #11 Mar 23 2021 15:43:13
%S 37,227,229,233,241,257,271,277,283,313,317,331,347,353,359,367,383,
%T 397,523,541,557,577,719,743,761,797,1117,1171,1361,1367,1373,1723,
%U 1741,1747,1753,1759,1783,1789,1973,1979,1997,2113,2131,2137,2179,2213,2239
%N Home primes whose homeliness is 2.
%C Number of terms < 10^n: 0, 1, 26, 182, 1428, 10395, 84164, ... .
%e Only {21 & 37} -> 37, 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 = 2 - 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, 50]
%Y Cf. A037274, A118756, A133957, A133956, A133960, 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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