OFFSET
1,1
COMMENTS
Numbers where a consecutive prime-difference (prime(a(n)+1)-prime(a(n))) arises with a new prime-power factor.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..64 (terms below 10^10)
EXAMPLE
From Michael De Vlieger, May 12 2017: (Start)
Values of A080374 starting at a(n).
n a(n) A080374(a(n))
1 2 1
2 4 2
3 9 4
4 24 12
5 30 24
6 34 168
7 99 840
8 189 2520
9 217 27720
10 282 471240
11 367 942480
12 738 12252240
13 3302 24504480
14 3427 465585120
15 3644 2327925600
16 3793 72165693600
17 4612 216497080800
18 7970 6278415343200
19 8688 144403552893600
20 14357 288807105787200
21 23283 12418705548849600
22 34202 509166927502833600
23 49414 18839176317604843200
24 85633 131874234223233902400
25 85787 6989334413831396827200
...
(End)
MATHEMATICA
s=1; Do[s1=s; s=LCM[s, Prime[n+1]-Prime[n]]; If[Greater[s, s1], Print[n]], {n, 1, 100000}]
(* Second program: *)
Most[Accumulate@ #2 + 1] & @@ Transpose@ Map[{First@ #, Length@ #} &, Split@ FoldList[LCM @@ {#1, #2} &, Differences@ Array[Prime, 10^4]]] (* Michael De Vlieger, May 12 2017 *)
PROG
(PARI) lista(pmax) = {my(k = 1, p1 = 2, lcmmax = 1, lcm1 = 1, d); forprime(p2 = 3, pmax, d = p2 - p1; lcm1 = lcm(lcm1, d); if(lcm1 > lcmmax, lcmmax = lcm1; print1(k, ", ")); p1 = p2; k++); } \\ Amiram Eldar, Jun 09 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 27 2003
EXTENSIONS
Edited by N. J. A. Sloane, May 13 2017 at the suggestion of Michael De Vlieger.
More terms from Amiram Eldar, Jun 09 2024
STATUS
approved