A308101 - OEIS

%I #20 Jun 25 2019 05:33:11

%S 46,1426,120842,12205042,1257119326,219043888774,37904185920914,

%T 8346405168610942,1610856197541911806,494532852645366924442,

%U 159830762776306031303126,63895498657264777378395106,25160765901619915831898554178,9890836489141547229675646151234

%N Numbers that set records for longest chains of "chained prime factors" of A308099.

%C Length          m       Distinct prime factors

%C ------     ----------   ----------------------

%C   2                46   {2,23}

%C   3              1426   {2,23,31}

%C   4            120842   {2,23,37,71}

%C   5          12205042   {2,23,37,71,101}

%C   6        1257119326   {2,23,37,71,101,103}

%C   7      219043888774   {2,23,37,71,101,131,137}

%C   8    37904185920914   {2,23,37,71,101,131,151,157}

%C   9  8346405168610942   {2,23,37,71,101,131,151,181,191}

%t ric[pr_,lp_,tg_] := Block[{cp}, If[tg==0, If[pr < curr, curr=pr], cp = NextPrime@ lp; While[pr cp^tg < curr, If[First@ IntegerDigits@ cp == Mod[lp, 10], ric[pr cp, cp, tg-1]]; cp = NextPrime@ cp]]]; a[n_] := Block[ {q = 2}, curr = Infinity; While[q^(n + 1) < curr, ric[q, q, n]; q = NextPrime@ q]; curr]; Array[a, 14] (* _Giovanni Resta_, Jun 25 2019 *)

%Y Cf. A308099, A308252.

%K nonn,base

%O 1,1

%A _Giorgos Kalogeropoulos_, May 12 2019

%E a(6)-a(14) from _Giovanni Resta_, Jun 25 2019