cp's OEIS Frontend

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.

Showing 1-4 of 4 results.

A040016 Largest prime < e^n.

Original entry on oeis.org

2, 7, 19, 53, 139, 401, 1093, 2971, 8101, 22013, 59863, 162751, 442399, 1202603, 3269011, 8886109, 24154939, 65659969, 178482289, 485165141, 1318815713, 3584912833, 9744803443, 26489122081, 72004899319, 195729609407, 532048240573, 1446257064289, 3931334297131
Offset: 1

Views

Author

Jud McCranie

Keywords

Comments

A050809 is a subset. Lim_{n --> infinity} a(n+1)/a(n) = e. - Jonathan Vos Post, May 02 2006

Examples

			a(20) = floor(e^20) - 54 = 485165195 - 54 = 485165141 as there are no primes p such that 485165141 < p < 485165195.

Links

Crossrefs

Cf. A000040, A000149, A007512, A014210, A050808, A050809, A059303, A064118, A095935, A115019, A074496, A118840.

Programs

Extensions

Edited by N. J. A. Sloane, Dec 22 2006
a(27)-a(29) from Giovanni Resta, Apr 29 2017

A117879 First semiprime after e^n.

Original entry on oeis.org

4, 4, 9, 21, 55, 155, 407, 1099, 2981, 8105, 22033, 59881, 162757, 442417, 1202611, 3269021, 8886117, 24154953, 65659981, 178482301, 485165203, 1318815739, 3584912849, 9744803447, 26489122131, 72004899341, 195729609431
Offset: 0

Views

Author

Jonathan Vos Post, May 02 2006

Keywords

Comments

Semiprime analog of A074496 = first prime after e^n. Lim_{n->infinity} a(n+1)/a(n) = e. There are numbers where floor(e^n) is itself a semiprime, as with floor(e^6) = 403 = 13 * 31, floor(e^15) = 3269017 = 773 * 4229, floor(e^20) = 485165195 = 5 * 97033039, floor(e^22) = 3584912846 = 2 * 1792456423, floor(e^24) = 26489122129 = 103 * 257175943.

Links

Crossrefs

Cf. A000040, A000149, A001358, A007512, A014210, A050808, A050809, A059303, A064118, A095935, A115019, A074496, A118840.

Programs

  • Mathematica
    fsa[n_]:=Module[{i=1,c=Floor[E^n]},While[PrimeOmega[c+i]!=2,i++];c+i]; Array[fsa,30,0] (* Harvey P. Dale, Oct 18 2013 *)

Formula

a(n) = Smallest semiprime > e^n. Smallest semiprime > floor(e^n). a(n) = min{s > A000149(n) and s in A001358}.

A117839 Primes of the form floor(Pi^k + e^k).

Original entry on oeis.org

2, 5, 17, 9255121991, 28870447577
Offset: 1

Views

Author

Jonathan Vos Post, Apr 30 2006

Keywords

Comments

Intersection of A000040 and A061675.
The next term has 1535 digits. - Harvey P. Dale, Apr 26 2011

Crossrefs

See also A059792 (Numbers k such that floor(Pi^k) is prime) and their corresponding primes A077547.
See also A059303 (Numbers k such that floor(e^k) + 1 is prime) and their corresponding primes A118840.
Cf. A000040, A059303, A059792, A061675, A077547, A074496.

Programs

  • Mathematica
    Select[Table[Floor[\[Pi]^n+E^n],{n,0,5000}],PrimeQ]  (* Harvey P. Dale, Apr 26 2011 *)

A117881 First semiprime after Pi^n.

Original entry on oeis.org

4, 4, 10, 33, 106, 309, 965, 3022, 9489, 29813, 93649, 294209, 924271, 2903678, 9122173, 28658147, 90032221, 282844574, 888582413, 2791563955, 8769956797, 27551631845, 86556004193, 271923706897, 854273519921, 2683779414319
Offset: 0

Views

Author

Jonathan Vos Post, May 02 2006

Keywords

Comments

Pi and semiprime analog of A074496 First prime after e^n. Lim_{n->infinity} a(n+1)/a(n) = Pi. See also A000796 Decimal expansion of Pi. There are numbers where floor(Pi^n) is itself a semiprime, as with floor(Pi^2) = 9, floor(Pi^6) = 961 = 31^2, floor(Pi^9) = 29809 = 13 * 2293, floor(Pi^25) = 2683779414317 = 5749 * 466825433.

Examples

			a(3) = 33 because Pi^3 = 31.0062766... floor(Pi^3) = 31 is prime hence 31 + 2 = 33 is a term.

Links

  • Eric Weisstein's World of Mathematics, e-Prime.

Crossrefs

Cf. A000040, A000149, A000796, A001358, A007512, A014210, A050808, A050809, A059303, A064118, A095935, A115019, A074496, A118840.

Programs

  • Mathematica
    fsp[n_]:=Module[{k=Ceiling[Pi^n]},While[PrimeOmega[k]!=2,k++];k]; Array[fsp,30,0]

Formula

a(n) = min{s in A001358 and s > Pi^n}.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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