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A002540
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Increasing gaps between prime-powers.
(Formerly M1431 N0565)
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7
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1, 5, 13, 19, 32, 53, 89, 139, 199, 293, 887, 1129, 1331, 5591, 8467, 9551, 15683, 19609, 31397, 155921, 360653, 370261, 492113, 1349533, 1357201, 2010733, 4652353, 17051707, 20831323, 47326693, 122164747, 189695659, 191912783
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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 (blekraj(AT)yahoo.com), Aug 03 2006
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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).
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LINKS
| Donovan Johnson, Table of n, a(n) for n=1..79 [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Nov 14 2008]
Index entries for primes, gaps between
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PROG
| Contribution from Michael Porter (michael_b_porter(AT)yahoo.com), Oct 31 2009: (Start)
(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)) (End)
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CROSSREFS
| Cf. A000961 (prime-powers), A057820 (gaps), A002386 (prime equivalent).
Sequence in context: A129919 A045454 A166575 * A082093 A045455 A160031
Adjacent sequences: A002537 A002538 A002539 * A002541 A002542 A002543
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Second term corrected by Donovan Johnson, Nov 13 2008 (cf. A094158).
a(28)-a(79) and b-file from Donovan Johnson (donovan.johnson(AT)yahoo.com), Nov 14 2008
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