A308101 Numbers that set records for longest chains of "chained prime factors" of A308099.

46, 1426, 120842, 12205042, 1257119326, 219043888774, 37904185920914, 8346405168610942, 1610856197541911806, 494532852645366924442, 159830762776306031303126, 63895498657264777378395106, 25160765901619915831898554178, 9890836489141547229675646151234

Offset

1,1

Comments

Length m Distinct prime factors

------ ---------- ----------------------

2 46 {2,23}

3 1426 {2,23,31}

4 120842 {2,23,37,71}

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

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

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

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

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

Links

Table of n, a(n) for n=1..14.

Mathematica

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 *)

Crossrefs

Cf. A308099, A308252.

Sequence in context: A103725 A332858 A264505 * A291129 A115608 A318044

Adjacent sequences: A308098 A308099 A308100 * A308102 A308103 A308104

Keyword

nonn,base

Author

Giorgos Kalogeropoulos, May 12 2019

Extensions

a(6)-a(14) from Giovanni Resta, Jun 25 2019

Status

approved