1,1

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.

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

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

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

Cf. A005113, A005109, A005110, A005111, A005112, A081424, A081425, A081426, A081427, A081428, A081429, A081430.

Cf. A082449, A129246, A081640, A129248.

Sequence in context: A103255 A031385 A126916 this_sequence A090424 A106974 A115374

Adjacent sequences: A056634 A056635 A056636 this_sequence A056638 A056639 A056640

more,nonn

Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 31 2001

Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 20 2003

More terms from Don Reble, Apr 11, 2003. 1432349099 < a(16) <= 25782283783.

a(16) and a(17) from M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Apr 21 2007