A074497 -id:A074497 - cp's OEIS frontend

A074496 a(n) = smallest prime > e^n.

2, 3, 11, 23, 59, 149, 409, 1097, 2999, 8111, 22027, 59879, 162779, 442439, 1202609, 3269029, 8886113, 24154957, 65660003, 178482319, 485165237, 1318815761, 3584912873, 9744803489, 26489122147, 72004899361, 195729609461, 532048240609, 1446257064299, 3931334297161

Offset: 0

Joseph L. Pe, Sep 26 2002

nonn

			The first prime > e^3 = 20.085... is 23, so a(3) = 23.

Amiram Eldar, Table of n, a(n) for n = 0..2302

Cf. A000040, A000149, A001113, A014210, A014211, A074497.

a[n_] := NextPrime[Exp[n]]; a /@ Range[0, 20] (* Giovanni Resta, Apr 03 2017 *)

for(n=1,50,print1(nextprime(exp(n))","))

Limmit_{n -> infinity} a(n+1)/a(n) = e. - Jonathan Vos Post, Apr 30 2006

More terms from Ralf Stephan, Mar 25 2003
Edited by N. J. A. Sloane, Dec 22 2006
a(18) inserted and more terms added by Amiram Eldar, Sep 30 2019

A061715 Numbers which are sandwiched between two numbers having the same ordered canonical form.

Original entry on oeis.org

4, 6, 12, 18, 30, 34, 42, 56, 60, 72, 86, 92, 94, 102, 108, 138, 142, 144, 150, 160, 180, 184, 186, 192, 198, 202, 204, 214, 216, 218, 220, 228, 236, 240, 248, 266, 270, 282, 300, 302, 304, 312, 320, 322, 328, 340, 348, 392, 394, 412, 414, 416, 420, 424, 432

Offset: 1

Amarnath Murthy, Aug 21 2002

The average of twin primes is a member. Is there ever a prime in the sequence?

The sequence does not contain odd numbers since the odd number would be sandwiched between 2k and 2k+2 = 2(k+1) for some k and one of k, k+1 is odd and the other even so the highest power of two dividing them cannot be the same. Since 2 is not in the sequence, there can be no primes. - Ray Chandler, Apr 13 2019

			34 is sandwiched between 33 and 35 which are of the form p*q where p and q are primes.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A074497, A074498.

isA061715 := proc(n)
    local nm1,np1 ;
    nm1 := ifactors(n-1)[2] ;
    np1 := ifactors(n+1)[2] ;
    if nops(nm1) = nops(np1) then
        for i from 1 to nops(nm1) do
            if op(2,op(i,nm1)) <>  op(2,op(i,np1)) then
                return false;
            end if;
        end do:
        true ;
    else
        false;
    end if;
end proc:
for n from 1 to 300 do
    if isA061715(n)  then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Jan 18 2017

f[n_] := Flatten[Table[{ # [[2]]}] & /@ FactorInteger[n]]; Drop[ Select[ Range[415], Sort[f[ # - 1]] == Sort[f[ # + 1]] & ], 1]

Edited and extended by Robert G. Wilson v, Aug 22 2002

A074460 Primes which are sandwiched between two numbers having the same unordered canonical form.

Original entry on oeis.org

19, 307, 349, 491, 739, 919, 1013, 1061, 1277, 1667, 1747, 2357, 2683, 3259, 3581, 3797, 3943, 4013, 4597, 4877, 4987, 5051, 5741, 6067, 7757, 9349, 9413, 9739, 9851, 9923, 9949, 10133, 10243, 10949, 11093, 11149, 12619, 12941, 12979, 13879, 14051

Offset: 1

Robert G. Wilson v, Aug 22 2002

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A074497, A074498, A061715.

Subsequence of A067889.

f[n_] := Flatten[Table[{ # [[2]]}] & /@ FactorInteger[n]]; Prime[ Select[ Range[1700], Sort[ f[ Prime[ # ] - 1]] == Sort[ f[ Prime[ # ] + 1]] & ]]

cp's OEIS Frontend

A074496 a(n) = smallest prime > e^n.

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A061715 Numbers which are sandwiched between two numbers having the same ordered canonical form.

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Maple

Mathematica

Extensions

A074460 Primes which are sandwiched between two numbers having the same unordered canonical form.

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Mathematica