

A056637


a(n) is the least prime of class n, according to the ErdősSelfridge classification of primes.


27



2, 11, 23, 47, 283, 719, 1439, 2879, 34549, 138197, 1266767, 14920303, 36449279, 377982107, 1432349099, 22111003847, 110874748763
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OFFSET

1,1


COMMENTS

A prime p is in class 1 if p1 has no prime factor larger than 3. If p1 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

Table of n, a(n) for n=1..17.


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 A106974 A198277
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



