Search: id:A056637
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%I A056637
%S A056637 2,11,23,47,283,719,1439,2879,34549,138197,1266767,14920303,36449279,
%T A056637 377982107,1432349099,22111003847,110874748763
%N A056637 a(n) is the least prime of class n-, according to the Erdos-Selfridge 
               classification of primes.
%C A056637 A prime p is in class 1- if p-1 has no prime factor larger than 3. If 
               p-1 has other prime factors, p is in class (c+1)-, where c- is the 
               largest class of its prime factors.
%C A056637 a(18) <= 619108107719, a(19) <= 19811459447009, a(20) <= 152772264735359. 
               These upper limits can be found by generating class (n+1)- primes 
               from a list of n- class primes; if the latter is sufficiently complete, 
               one can deduce that there is no smaller (n+1)- prime. - M. F. Hasler 
               (Maximilian.Hasler(AT)gmail.com), Apr 05 2007
%F A056637 a(n+1) >= 2*a(n)+1, since a(n+1)-1 is even and must have a factor of 
               class n- which is odd (n>1) and >= a(n). a(n+1) <= min { p = 2*k*a(n)+1 
               | k=1,2,3... such that p is prime }, since a(n) is a prime of class 
               n-. - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Apr 05 2007
%t A056637 PrimeFactors[n_Integer] := Flatten[ Table[ #[[1]], {1}] & /@ FactorInteger[n]]; 
               NextPrime[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; 
               f[n_Integer] := Block[{m = n}, If[m == 0, m = 1, While[ IntegerQ[m/
               2], m /= 2]; While[ IntegerQ[m/3], m /= 3]]; Apply[Times, PrimeFactors[m] 
               - 1]]; ClassMinusNbr[n_] := Length[NestWhileList[f, n, UnsameQ, All]] 
               - 3; a = Table[0, {15}]; a[[1]] = 2; k = 5; Do[c = ClassMinusNbr[ 
               k]; If[ a[[c]] == 0, a[[c]] = k]; k = NextPrime[k], {n, 3, 7223000}]; 
               a
%Y A056637 Cf. A005113, A005109, A005110, A005111, A005112, A081424, A081425, A081426, 
               A081427, A081428, A081429, A081430.
%Y A056637 Cf. A082449, A129246, A081640, A129248.
%Y A056637 Sequence in context: A103255 A031385 A126916 this_sequence A090424 A141423 
               A106974
%Y A056637 Adjacent sequences: A056634 A056635 A056636 this_sequence A056638 A056639 
               A056640
%K A056637 more,nonn
%O A056637 1,1
%A A056637 Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 31 2001
%E A056637 Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 20 2003
%E A056637 More terms from Don Reble, Apr 11, 2003. 1432349099 < a(16) <= 25782283783.
%E A056637 a(16) and a(17) from M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Apr 
               21 2007

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