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%I M1431 N0565 #47 Dec 12 2022 01:32:51
%S 1,5,13,19,32,53,89,139,199,293,887,1129,1331,5591,8467,9551,15683,
%T 19609,31397,155921,360653,370261,492113,1349533,1357201,2010733,
%U 4652353,17051707,20831323,47326693,122164747,189695659,191912783
%N Increasing gaps between prime-powers.
%C List of prime-powers where A057820 increases.
%C 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
%D 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.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Donovan Johnson, <a href="/A002540/b002540.txt">Table of n, a(n) for n = 1..79</a>
%H J. P. Gram, <a href="/A002540/a002540_1.pdf">Undersoegelser angaaende maengden af primtal under en given graense</a> (1884) [Scanned copy of page 255 with annotations by Victor Meally and N. J. A. Sloane]
%H Des MacHale and Joseph Manning, <a href="https://www.jstor.org/stable/24496947">Maximal runs of strictly composite integers</a>, The Mathematical Gazette, Vol. 99, No. 545 (2015), pp. 213-219.
%H Victor Meally, <a href="/A002540/a002540.pdf">Letter to N. J. A. Sloane, Mar 17, 1980</a>.
%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>.
%t 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 *)
%o (PARI) /* calculates smaller terms - see Donovan Johnson link for larger terms */
%o isA000961(n) = (omega(n) == 1 || n == 1)
%o 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
%Y Cf. A000961 (prime-powers), A057820 (gaps), A002386 (prime equivalent), A094158, A121493.
%K nonn,nice
%O 1,2
%A _N. J. A. Sloane_
%E Second term corrected by _Donovan Johnson_, Nov 13 2008 (cf. A094158)
%E a(28)-a(79) and b-file from _Donovan Johnson_, Nov 14 2008
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