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%I #15 Apr 03 2024 15:15:38
%S 2,11,23,47,283,719,1439,2879,34549,138197,1266767,14920303,36449279,
%T 377982107,1432349099,22111003847,110874748763
%N a(n) is the least prime of class n-, according to the Erdős-Selfridge classification of primes.
%C 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. See also A005109.
%C 1432349099 < a(16) <= 25782283783.
%C 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_, Apr 05 2007
%F 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_, Apr 05 2007
%t 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 Cf. A005113, A005109, A005110, A005111, A005112, A081424, A081425, A081426, A081427, A081428, A081429, A081430.
%Y Cf. A082449, A129246, A081640, A129248.
%K more,nonn
%O 1,1
%A _Robert G. Wilson v_, Jan 31 2001
%E Extended by _Robert G. Wilson v_, Mar 20 2003
%E More terms from _Don Reble_, Apr 11 2003
%E a(16) and a(17) from _M. F. Hasler_, Apr 21 2007
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