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 A112037 Go through all of the primes p and for each one, factor p-1 into primes. List the primes in order of their first appearance in the p-1 factorizations. 6
 2, 3, 5, 11, 7, 23, 13, 29, 41, 17, 53, 37, 83, 43, 89, 19, 113, 131, 67, 47, 73, 31, 79, 173, 179, 61, 191, 97, 233, 239, 251, 127, 139, 281, 71, 293, 101, 103, 107, 163, 59, 359, 193, 199, 137, 419, 431, 443, 151, 491, 509, 181, 109, 277, 593, 149, 307, 641, 653 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The length of this list of distinct prime factors of p-1 encountered through p=prime(n) is given by A055768. - Ray Chandler, Nov 30 2005 If "p-1" is changed to "p+1" we get A236388. - N. J. A. Sloane, Jan 24 2014 A permutation of the primes by Dirichlet's theorem on arithmetic progressions: for any pair (r,s) of integers such that gcd(r,s)=1 there are infinitely many primes in the sequence r + k*s; choose r=1 and s=p. - Joerg Arndt, Mar 20 2016 LINKS Alois P. Heinz, Table of n, a(n) for n = 2..10000 EXAMPLE We start with the second prime, 3. 3-1 = 2, so 2 is the first term. 5-1 = 2*2, nothing new. 7-1 = 2*3 and 3 is new, so that is the second term. 11-1 = 2*5 and we get 5; etc. MATHEMATICA lst = {}; r[n_] := (len = Length@lst; lst = Flatten@ Join[lst, Select[First /@ FactorInteger[Prime@n - 1], ! MemberQ[lst, # ] &]]; If[l < Length@lst, 1, 0]); Do[ r[n], {n, 214}]; lst (* Robert G. Wilson v, Nov 30 2005 *) DeleteDuplicates[Rest[Flatten[FactorInteger[#][[All, 1]]&/@ (Prime[ Range[ 250]]-1)]]] (* Harvey P. Dale, May 26 2019 *) PROG (PARI) g=1; forprime(p=2, 299, f=factorint(p-1)[, 1]; z=factorback(f); r=z/gcd(z, g); g*=r; if(r>1, print(r, " ", p))); \\ Jack Brennen, Nov 28 2005 (GAP) Set(Flat(List(Filtered([3..1500], IsPrime), i->Factors(i-1)))); # Muniru A Asiru, Dec 06 2018 CROSSREFS Cf. A055768, A112038, A114461, A236388. Sequence in context: A084333 A288833 A067663 * A087583 A233098 A258975 Adjacent sequences:  A112034 A112035 A112036 * A112038 A112039 A112040 KEYWORD easy,nonn AUTHOR Michel Dauchez (mdzdm(AT)yahoo.fr), Nov 28 2005 EXTENSIONS Better description from Jack Brennen, Nov 28 2005 Extended by Ray Chandler and Robert G. Wilson v, Nov 30 2005 STATUS approved

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Last modified July 12 13:27 EDT 2020. Contains 335663 sequences. (Running on oeis4.)