%I A118756
%S A118756 2,23,211,379,773,3389,23251,3761,178069,77773,379811,378997,747521,
%T A118756 2337691,3789293,3574657
%N A118756 Define a function f on the set of primes as follows: f(p) = the cardinality 
               of the set {n | p is the home prime of n} (cf. A037274). Then a(n) 
               = smallest prime such that f(p) = n.
%C A118756 In other words, the smallest prime p such that p is the home prime of 
               exactly n natural numbers.
%e A118756 23 is the home prime of both 6 and 23, thus a(2) = 23; 211 is the home 
               prime of 6, 22 and 211, thus a(3) = 211.
%e A118756 More compactly: (2) -> 2, (6,23) -> 23, (4,22,211) -> 211,
%e A118756 (42,74,237,379) -> 379, (10,25,55,511,773) -> 773,
%e A118756 (118, 259, 737, 801, 1167, 3389) -> 3389,
%e A118756 {250, 1506, 2555, 3865, 5773, 6502, 23251} -> 23251,
%e A118756 {140, 332, 514, 566, 1281, 2257, 2283, 3761} -> 3761,
%e A118756 {4206, 7402, 10786, 16123, 23701, 25393, 67379, 137173, 178069} -> 178069,
%e A118756 {3786, 7262, 10078, 14513, 18417, 23631, 25039, 32449, 37877, 77773} 
               -> 77773,
%e A118756 {41933, 50161, 56598, 103487, 192207, 206031, 216959, 239433, 307369, 
               363007, 379811} -> 379811,
%e A118756 {1798, 5982, 22931, 23997, 41315, 53033, 58263, 181293, 184102, 292051, 
               319421, 378997} -> 378997,
%e A118756 {722, 4938, 5718, 7646, 18929, 21919, 23823, 23953, 91277, 97941, 171409, 
               332647, 747521} -> 747521,
%e A118756 {87066, 128055, 138438, 153402, 175611, 226146, 358537, 465734, 588041, 
               675382, 866893, 1792003, 1564051, 2337691} -> 2337691,
%e A118756 {8691, 9725, 23585, 31437, 32897, 55389, 67491, 144995, 168163, 337499, 
               547617, 964849, 1875153, 3303841, 3789293} -> 3789293,
%e A118756 {5978, 10654, 27761, 40307, 47985, 111855, 156657, 172371, 202881, 250519, 
               357457, 379661, 407507, 488985, 1723971, 3574657} -> 3574657, etc. 
               - Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 01 2007
%t A118756 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, 10^7}];
%t A118756 lst = Sort@ lst; Table[d = n - 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}]; First@ Union@ lsu, 
               {n, 3, 16}] - Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 01 2007
%Y A118756 Cf. A037274, A133956, A133958, A133960, A133962, A133964, A133966, A133968, 
               A133970, A133972, A133974, A133976, A133978.
%Y A118756 Sequence in context: A041579 A053299 A130547 this_sequence A133955 A062600 
               A069590
%Y A118756 Adjacent sequences: A118753 A118754 A118755 this_sequence A118757 A118758 
               A118759
%K A118756 nonn
%O A118756 1,1
%A A118756 William Lindgren (william.lindgren(AT)sru.edu), Sep 04 2007, corrected 
               Sep 15 2007
%E A118756 a(7)-a(16) from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 27 2007, Oct 
               01 2007
%E A118756 a(17) > 10^7, a(18) = 3784463 - Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Oct 01 2007