A133956 - OEIS

%I #10 Mar 23 2021 15:43:05

%S 2,3,5,7,11,13,17,19,29,31,41,43,47,53,59,61,67,71,73,79,83,89,97,101,

%T 103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,

%U 193,197,199,239,251,263,269,281,293,307,349,401,409,419,421,431,433

%N Complement of A133957.

%C Home primes whose homeliness is 1.

%C Number of terms < 10^n: Pi(10^n)- {0, 2, 37, 274, 2087, 15472, 76940, ...}.

%e Only {2} -> 2, {3} -> 3, etc. Whereas {6 & 23} -> 23 thus 23 has a homeliness of 2 and therefore is not a member of this sequence.

%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 Complement[ Prime@ Range@ 100, {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}]

%Y Cf. A037274, A118756, A133957, A133958, A133960, A133962, A133964, A133966, A133968, A133970, A133972, A133974, A133976, A133978.

%K nonn,base

%O 1,1

%A _Robert G. Wilson v_, Sep 30 2007