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 A056637 a(n) is the least prime of class n-, according to the Erdős-Selfridge classification of primes. 27
 2, 11, 23, 47, 283, 719, 1439, 2879, 34549, 138197, 1266767, 14920303, 36449279, 377982107, 1432349099, 22111003847, 110874748763 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. 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 LINKS FORMULA 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 MATHEMATICA 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 CROSSREFS Cf. A005113, A005109, A005110, A005111, A005112, A081424, A081425, A081426, A081427, A081428, A081429, A081430. Cf. A082449, A129246, A081640, A129248. Sequence in context: A179878 A126916 A090424 * A141423 A344032 A338225 Adjacent sequences: A056634 A056635 A056636 * A056638 A056639 A056640 KEYWORD more,nonn AUTHOR Robert G. Wilson v, Jan 31 2001 EXTENSIONS Extended by Robert G. Wilson v, Mar 20 2003 More terms from Don Reble, Apr 11, 2003. 1432349099 < a(16) <= 25782283783. a(16) and a(17) from M. F. Hasler, Apr 21 2007 STATUS approved

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Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)