A092250 -id:A092250 - cp's OEIS frontend

A092245 Lesser of the first twin prime pair with n digits.

3, 11, 101, 1019, 10007, 100151, 1000037, 10000139, 100000037, 1000000007, 10000000277, 100000000817, 1000000000061, 10000000001267, 100000000000097, 1000000000002371, 10000000000001549, 100000000000000019

Offset: 1

Cino Hilliard, Feb 17 2004

Sum of reciprocals = 0.43523579465477...

Robert G. Wilson v, Table of n, a(n) for n = 1..1000 First 101 from _Abhiram R Devesh_

Cf. A092250, A124001.

for n from 1 to 100 do
  r:= 10^(n-1);
  p:= nextprime(r); q:= nextprime(p);
  while q - p > 2 do
    p:= q; q:= nextprime(p);
  od;
  A[n]:= p;
od:
seq(A[n],n=1..100); # Robert Israel, Aug 04 2014

a[n_] := Block[{p = NextPrime[10^(n -1)]}, While[ !PrimeQ[p +2], p = NextPrime@ p]; p]; Array[a, 18] (* Robert G. Wilson v, Dec 04 2022 *)

firsttwpr(n) = { sr=0; for(m=0,n, c=0; for(x=10^m+1,10^(m+1), if(isprime(x)&& isprime(x+2),print1(x",");sr+=1./x;break) ) ); print(); print(sr) }

import sympy
for i in range(100):
    p=sympy.nextprime(10**i)
    while not sympy.isprime(p+2):
        p=sympy.nextprime(p)
    print(p)
# Abhiram R Devesh, Aug 02 2014

a(n) = A124001(n-1) + 10^(n-1). - Robert G. Wilson v, Nov 28 2015

Corrected by T. D. Noe, Nov 15 2006

A114429 Larger of the greatest twin prime pair with n digits.

Original entry on oeis.org

7, 73, 883, 9931, 99991, 999961, 9999973, 99999589, 999999193, 9999999703, 99999999763, 999999999961, 9999999998491, 99999999999973, 999999999997969, 9999999999999643, 99999999999998809, 999999999999998929

Offset: 1

Cino Hilliard, Feb 13 2006

Also the denominator of the largest prime over prime fraction less than 10^n.

Abhiram R Devesh, Table of n, a(n) for n = 1..100

Cf. A092250 (a(n)-2: lesser of the pair).

Table[i=1;Until[PrimeQ[10^n-i]&&PrimeQ[10^n-i-2],i++];10^n-i,{n,18}] (* James C. McMahon, Jul 31 2024 *)

a(n)=my(p=precprime(10^n)); while(!ispseudoprime(p-2),p=precprime(p-1)); return(p)
vector(50, n, a(n)) \\ Derek Orr, Aug 02 2014

apply( {A114429(n,p=10^n)=until(2==p-p=precprime(p-1),);p+2}, [1..22]) \\ twice as fast by avoiding additional ispseudoprime(). - M. F. Hasler, Jan 17 2022

import sympy
for i in range(1,100):
    p=sympy.prevprime(10**i)
    while not sympy.isprime(p-2):
        p=sympy.prevprime(p)
    print(p)
# Abhiram R Devesh, Aug 02 2014

from sympy import prevprime
def a(n):
    p = prevprime(10**n); pp = prevprime(p)
    while p - pp != 2: p, pp = pp, prevprime(pp)
    return p
print([a(n) for n in range(1, 19)]) # Michael S. Branicky, Jan 17 2022

a(n) = A092250(n) + 2. - M. F. Hasler, Jan 17 2022

Corrected by T. D. Noe, Nov 15 2006

A327133 The difference between 10^n and the lesser of the twin primes immediately before.

Original entry on oeis.org

5, 29, 119, 71, 11, 41, 29, 413, 809, 299, 239, 41, 1511, 29, 2033, 359, 1193, 1073, 1499, 2261, 5003, 2429, 1793, 4331, 833, 5879, 359, 779, 2813, 1061, 2099, 1811, 3281, 5201, 533, 5483, 1679, 1421, 26801, 12089, 2843, 27773, 9641, 10841, 4763, 2129, 1019, 20531, 8519, 14339

Offset: 1

Robert G. Wilson v, Nov 28 2019

nonn

All terms are congruent to 5 (mod 6).

Records: 5, 29, 119, 413, 809, 1511, 2033, 2261, 5003, 5879, 26801, ..., 37058441, ... - Robert G. Wilson v, Dec 10 2019

			a(1) = 5 because the greatest twin prime pair less than 10 is {5, 7};
a(2) = 29 since the greatest 2-digit twin prime pair is {71, 73};
a(3) = 119 since the greatest 3-digit twin prime pair is {881, 883}; etc.

Robert G. Wilson v, Table of n, a(n) for n = 1..1250

Cf. A011557, A092250.

f:= proc(n) local w,p,q;
w:= 10^n; q:= w;
do
  p:= q;
  q:= prevprime(p);
  if p-q = 2 then return w-q fi;
od
end proc:
map(f, [$1..100]); # Robert Israel, Nov 28 2019

p[n_] := Block[{d = PowerMod[10, n, 6]}, 10^n - NestWhile[# -6 &, 10^n -d -1, !PrimeQ[#] || !PrimeQ[# +2] &]]; Array[p, 50] (* updated Nov 29 2019 *)

prectwin(n)=n++; while(!isprime(2+n=precprime(n-1)),); n
a(n)=10^n - prectwin(10^n) \\ Charles R Greathouse IV, Nov 28 2019

a(n) = A011557(n) - A092250(n).

cp's OEIS Frontend

A092245 Lesser of the first twin prime pair with n digits.

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A114429 Larger of the greatest twin prime pair with n digits.

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Author

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Comments

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Crossrefs

Programs

Mathematica

PARI

PARI

Python

Python

Formula

Extensions

A327133 The difference between 10^n and the lesser of the twin primes immediately before.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula