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A133956
Complement of A133957.
12
2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 239, 251, 263, 269, 281, 293, 307, 349, 401, 409, 419, 421, 431, 433
OFFSET
1,1
COMMENTS
Home primes whose homeliness is 1.
Number of terms < 10^n: Pi(10^n)- {0, 2, 37, 274, 2087, 15472, 76940, ...}.
EXAMPLE
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.
MATHEMATICA
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}];
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}]
KEYWORD
nonn,base
AUTHOR
Robert G. Wilson v, Sep 30 2007
STATUS
approved