A095935 -id:A095935 - cp's OEIS frontend

A040016 Largest prime < e^n.

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

Jud McCranie

nonn

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

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

Giovanni Resta, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, e-Prime.

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

Table[NextPrime[E^n,-1],{n,30}] (* Harvey P. Dale, Jul 24 2016 *)

a(n)=precprime(exp(n)) \\ Charles R Greathouse IV, Mar 26 2013

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

Jonathan Vos Post, May 02 2006

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.

Harvey P. Dale, Table of n, a(n) for n = 0..100
Eric Weisstein's World of Mathematics, e-Prime.

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

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 *)

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

A198188 Primes from the decimal expansion of e, sorted first by the final digit index and then by length.

Original entry on oeis.org

2, 7, 71, 271, 2, 281, 2718281, 2, 5, 59, 5, 2, 3, 23, 523, 4523, 904523, 5, 3, 53, 353, 8284590452353, 2, 7, 360287, 28459045235360287, 7, 47, 8747, 6028747, 8182845904523536028747, 71, 360287471, 8281828459045235360287471, 3, 13, 74713, 82818284590452353602874713

Offset: 1

Franklin T. Adams-Watters, Oct 21 2011

			The first digit, 2, is prime, so a(1) = 2.
The second digit, 7, is prime, so a(2) = 7. 27 is not prime.
The third digit, 1, is not prime, but 71 and 271 are, so a(3) = 71 and a(4) = 271.
a(17) shows that "leading zeros are not allowed", i.e., if a prime p is prefixed by a 0 then it is not listed twice. - _M. F. Hasler_, Feb 05 2012

M. F. Hasler, Table of n, a(n) for n = 1..655

Cf. A095935.

v=[2, 7, 1, 8, 2, 8, 1, 8, 2, 8, 4, 5, 9, 0, 4, 5, 2, 3, 5, 3, 6, 0, 2, 8, 7, 4, 7, 1, 3]
for(n=1, #v, x=0; p=1; forstep(k=n, 1, -1, x+=p*v[k]; p*=10; if(v[k]&&isprime(x), print1(x", "))))

default(realprecision,D=300);for(i=0,D-5,E=exp(1)\.1^i;for(j=1,i+1,ispseudoprime(t=E%10^j) & t!=L print1(L=t",")))  \\ M. F. Hasler, Feb 05 2012

A137443 First n-digit prime in consecutive digits of e.

Original entry on oeis.org

7, 71, 281, 4523, 74713, 904523, 6028747, 72407663, 360287471, 7427466391, 75724709369, 749669676277, 8284590452353, 99959574966967, 724709369995957, 2470936999595749, 28459045235360287, 571382178525166427

Offset: 1

Dan Drake, Apr 18 2008

If the "2" at the beginning of e is included, the only values for n <= 1000 that change are a(1) = 2, a(3) = 271 and a(85) = 2718281828459045235360287471352662497757247093699959574966967627724076630353547594571.

For another version starting with 2 see A095935. - Omar E. Pol, Oct 24 2011

			7427466391 is the first 10-digit prime found in consecutive digits of e, so a(10) = 7427466391.

Dan Drake, Table of n, a(n) for n = 1..1000
Pegg, E. Jr. and Weisstein, E. W. Mathematica's Google Aptitude. MathWorld Headline news, Oct 13, 2004.

Cf. A095926.

Cf. A001113, A095935. - Omar E. Pol, Oct 24 2011

def a(digits):
    bits = 0
    pos = 0
    while True:
        bits += (digits * 4) + 50
        decimals = RealField(bits, rnd='RNDZ')(exp(1)).frac().str()[2:]
        for s in range(pos, len(decimals) - digits + 1):
            if decimals[s] != '0':
                i = Integer(decimals[s:s+digits])
                if i.is_prime():
                    return i
        pos = len(decimals) - digits + 1

A186208 The first n-digit prime in the decimal expansion of 1/e.

Original entry on oeis.org

3, 67, 367, 7879, 36787, 367879, 8794411, 21595523, 867445811, 2159552377, 23215955237, 794411714423, 9441171442321, 57147274345919, 767834507836801, 4581113103176783, 67834507836801697, 595523770161460867, 3176783450783680169

Offset: 1

Michel Lagneau, Feb 15 2011

1/e = 0.36787944117144232159....

Matthew House, Table of n, a(n) for n = 1..996

Cf. A001113, A095935.

Digits := 10000: p0 := evalf(1/exp(1))*10:for d from 1 to 20 do: id:=0:for
  i from 0 to 50000 while(id=0) do :q0:=trunc(p0*10^(i+d-1)): x:= irem(q0,10^d):
  if type(x,prime)=true and length(x)=d then printf(`%d, `,x):id:=1: else fi:od:od:

With[{x=RealDigits[1/E,10,1000][[1]]},Table[FromDigits[ First[ Select[ Partition[x,n,1],PrimeQ[FromDigits[#]]&]]],{n,20}]]  (* Harvey P. Dale, Feb 17 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

Jonathan Vos Post, May 02 2006

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.

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

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

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

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

a(n) = min{s in A001358 and s > Pi^n}.

cp's OEIS Frontend

A040016 Largest prime < e^n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A117879 First semiprime after e^n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A198188 Primes from the decimal expansion of e, sorted first by the final digit index and then by length.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

PARI

A137443 First n-digit prime in consecutive digits of e.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Sage

A186208 The first n-digit prime in the decimal expansion of 1/e.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

A117881 First semiprime after Pi^n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula