OFFSET
1,2
COMMENTS
List of prime-powers where A057820 increases.
The entry K=a(k) is the start of the smallest chain of m=A121492(k) consecutive numbers such that lcm(1,2,...,K) = lcm(1,2,...,K,K+1) = lcm(1,2,...,K,K+1,K+2) = ... = lcm(1,2,...,K,...,K+m-1). See A121493. - Lekraj Beedassy, Aug 03 2006
REFERENCES
J. P. Gram, Undersoegelser angaaende maengden af primtal under en given graense, Det Kongelige Danskevidenskabernes Selskabs Skrifter, series 6, vol. 2 (1884), 183-288; see p. 255.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..79
J. P. Gram, Undersoegelser angaaende maengden af primtal under en given graense (1884) [Scanned copy of page 255 with annotations by Victor Meally and N. J. A. Sloane]
Des MacHale and Joseph Manning, Maximal runs of strictly composite integers, The Mathematical Gazette, Vol. 99, No. 545 (2015), pp. 213-219.
Victor Meally, Letter to N. J. A. Sloane, Mar 17, 1980.
MATHEMATICA
s = {}; gap = 0; p1 = 1; Do[If[PrimePowerQ[p2], If[(d = p2 - p1) > gap, gap = d; AppendTo[s, p1]]; p1 = p2], {p2, 2, 10^6}]; s (* Amiram Eldar, Dec 12 2022 *)
Join[{1}, Rest[Module[{nn=5*10^6, pps}, pps=Select[Range[nn], PrimePowerQ]; DeleteDuplicates[ Thread[{Most[ pps], Differences[ pps]}], GreaterEqual[ #1[[2]], #2[[2]]]&]][[;; , 1]]]] (* The program generates the first 27 terms of the sequence. *) (* Harvey P. Dale, Aug 20 2024 *)
PROG
(PARI) /* calculates smaller terms - see Donovan Johnson link for larger terms */
isA000961(n) = (omega(n) == 1 || n == 1)
d_max=0; n_prev=1; for(n=2, 1e6, if(isA000961(n), d=n-n_prev; if(d>d_max, print(n_prev); d_max=d); n_prev=n)) \\ Michael B. Porter, Oct 31 2009
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
Second term corrected by Donovan Johnson, Nov 13 2008 (cf. A094158)
a(28)-a(79) and b-file from Donovan Johnson, Nov 14 2008
STATUS
approved