A133964 - OEIS

%I #11 Mar 23 2021 15:42:28

%S 773,1129,3137,3251,3593,3797,7541,7853,23167,23557,23719,23743,23773,

%T 23971,31973,33191,33331,33769,33863,37307,37573,37691,37997,39733,

%U 39929,47797,53101,61613,67349,67709,71129,71171,71443,71719,73181

%N Home primes whose homeliness is 5.

%C Number of terms < 10^n: 0, 0, 1, 8, 44, 417, 3299, ... .

%e Only (10, 25, 55, 511, 773) -> 773, 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 = 5 - 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, A133963, A133956, A133957, A133958, A133960, A133962, A133966, A133968, A133970, A133972, A133974, A133976, A133978.

%K nonn,base

%O 1,1

%A _Robert G. Wilson v_, Sep 30 2007