A069100 -id:A069100 - cp's OEIS frontend

A073914 Triangle read by rows in which row n gives n smallest n-digit primes.

2, 11, 13, 101, 103, 107, 1009, 1013, 1019, 1021, 10007, 10009, 10037, 10039, 10061, 100003, 100019, 100043, 100049, 100057, 100069, 1000003, 1000033, 1000037, 1000039, 1000081, 1000099, 1000117

Offset: 0

Amarnath Murthy, Aug 18 2002

a((k-1)*k/2) is the smallest k-digit prime.

Main diagonal gives A069100.

Edited by Don Reble, Jun 15 2003

A107108 Shorthand of n-th smallest n-digit prime, see comments.

Original entry on oeis.org

2, 3, 7, 21, 61, 69, 117, 189, 193, 181, 259, 193, 303, 411, 487, 513, 931, 591, 861, 667, 801, 1081, 711, 1027, 1321, 1753, 1581, 2109, 1527, 1951, 2613, 2053, 2533, 3171, 2653, 3073, 2769, 2899, 3201, 3133, 4089, 2859, 4447, 5367, 3819, 4923, 5251, 5109, 5127, 6721

Offset: 1

Zak Seidov, May 12 2005

To shorthand the n-th - smallest n-digit prime it is convenient to subtract 10^(n-1) (n>1). Compare a(n) with A069100(n).

David A. Corneth, Table of n, a(n) for n = 1..1000 (using b-file from A069100)

Cf. A069100.

a(n)=prime(primepi(10^(n-1))+n)-if(n==1,0,10^(n-1)) \\ Franklin T. Adams-Watters, Mar 07 2014

a(n) = {if(n == 1, return(2)); my(t = 0); forprime(p = 10^(n-1), 10^n, t++; if(t==n, return(p - 10^(n-1))))} \\ David A. Corneth, Jun 16 2021

from sympy import nextprime
def a(n):  return nextprime(10**(n-1), ith=n) - 10**(n-1) * (n > 1)
print([a(n) for n in range(1, 51)]) # Michael S. Branicky, Jun 16 2021

a(1)=2; at n>1 a(n)=prime(pi[10^(n-1)]+n)-10^(n-1)=A069100(n)-10^(n-1).

a(3) corrected by Franklin T. Adams-Watters, Mar 07 2014

More terms from David A. Corneth, Jun 16 2021

A107109 n-th largest n-digit prime.

Original entry on oeis.org

7, 89, 983, 9941, 99929, 999931, 9999929, 99999827, 999999739, 9999999769, 99999999763, 999999999697, 9999999999443, 99999999999503, 999999999999353, 9999999999999431, 99999999999999251, 999999999999999463, 9999999999999999343, 99999999999999999199

Offset: 1

Zak Seidov, May 12 2005

Cf. A069100: n-th smallest n-digit prime.

Eduard Roure Perdices, Table of n, a(n) for n = 1..1000

Cf. A069100.

Table[Prime[PrimePi[10^n]-n+1], {n, 13}]
a[n_] := NextPrime[10^n, -n]; (* Eduard Roure Perdices, May 09 2021 *)

a(n) = prime[pi[10^n]-n+1]

Extended by Eduard Roure Perdices, May 09 2021

cp's OEIS Frontend

A073914 Triangle read by rows in which row n gives n smallest n-digit primes.

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A107108 Shorthand of n-th smallest n-digit prime, see comments.

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A107109 n-th largest n-digit prime.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions