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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A058017 a(n) is the smallest prime > LCM(1,...,x), where x is the n-th prime power (A000961).

Original entry on oeis.org

2, 3, 7, 13, 61, 421, 853, 2521, 27733, 360391, 720743, 12252259, 232792561, 5354228921, 26771144401, 80313433231, 2329089562843, 72201776446801, 144403552893641, 5342931457063253, 219060189739591279, 9419588158802421659, 442720643463713815201, 3099044504245996706459
Offset: 1

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Author

Labos Elemer, Nov 14 2000

Keywords

Comments

For the first 100 prime powers, the difference between a(n) and the LCM is either 1 or a prime.
The values of x are taken to be prime powers so that each distinct LCM occurs exactly once.

Examples

			The 6th distinct prime power is A000961(7) = 8, LCM(1,...,8) = 840 and 853 is the first prime that follows, thus a(7) = 853.

Crossrefs

Cf. A000961, A003418, A051451, A058018, A151800.

Programs

  • Mathematica
    With[{max = 50}, NextPrime[Exp[Accumulate[Join[{0}, Select[Array[MangoldtLambda, max], # > 0 &]]]]]] (* Amiram Eldar, Aug 13 2024 *)
  • PARI
    lista(nn) = {for (n=1, nn, if ((n==1) || isprimepower(n), print1(nextprime(lcm(vector(n, x, x)) + 1), ", ")));} \\ Michel Marcus, Apr 09 2015

Formula

a(n) = A151800(A051451(n)) = A051451(n) + A058018(n). - Amiram Eldar, Aug 13 2024

Extensions

Edited by Franklin T. Adams-Watters, Aug 15 2006
Offset changed to 1 and more terms from Michel Marcus, Apr 09 2015
Name corrected by Amiram Eldar, Aug 13 2024
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