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%I #11 Mar 23 2021 15:41:44
%S 77773,312619,359929,364627,374531,749711,771941,1355021,1389281,
%T 1929311,1991153,2336263,2337547,2339929,2373823,2389853,2397127,
%U 3137993,3139547,3139733,3139907,3235471,3312539,3313631,3316661
%N Home primes whose homeliness is 10.
%C Number of terms < 10^n: 0, 0, 0, 0, 1, 7, 82, ... .
%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 = 10 - 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, 35]
%Y Cf. A037274, A118756, A133973, A133956, A133957, A133958, A133960, A133962, A133964, A133966, A133968, A133970, A133972, A133976, A133978.
%K nonn,base
%O 1,1
%A _Robert G. Wilson v_, Sep 30 2007
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