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.

A070854 Smallest prime == 1 mod (10^n).

Original entry on oeis.org

11, 101, 3001, 70001, 700001, 22000001, 30000001, 600000001, 6000000001, 30000000001, 1900000000001, 18000000000001, 40000000000001, 3900000000000001, 6000000000000001, 130000000000000001, 3700000000000000001, 15000000000000000001, 150000000000000000001, 600000000000000000001, 16000000000000000000001
Offset: 1

Views

Author

Amarnath Murthy, May 15 2002

Keywords

Comments

a(6) through a(21) have been certified prime with Primo. - Rick L. Shepherd, Jun 03 2002

Crossrefs

Cf. A070846 to A070853.

Programs

  • PARI
    a(n)=for(i=1,+oo,if(isprime(i*10^n+1), return(i*10^n+1))) \\ Johann Peters, Dec 27 2024

Formula

a(n) = A121172(n)*10^n + 1. - Ray Chandler, Feb 10 2009

Extensions

More terms from Rick L. Shepherd, Jun 03 2002

A120124 Smallest prime p such that p*10^n + 1 is a prime.

Original entry on oeis.org

3, 7, 3, 7, 7, 61, 3, 7, 7, 3, 19, 37, 109, 79, 97, 13, 37, 19, 73, 103, 97, 283, 157, 61, 19, 61, 1213, 3, 163, 691, 367, 163, 181, 157, 241, 3, 103, 733, 151, 283, 337, 193, 211, 163, 7, 73, 307, 61, 223, 1549, 31, 127, 13, 547, 103, 151, 193, 811, 337, 19, 1021, 151
Offset: 1

Views

Author

Alexander Adamchuk, Aug 15 2006

Keywords

Comments

All terms belong to A007645. All terms also belong to A055664. Also many terms including the first 14 smallest primes from 3 to 139 {3,7,13,19,31,37,43,61,73,79,97,103,127,139} belong tpA023203. The smallest term that differs from A023203 is 151.

Examples

			a(1) = 3 because 31 = 3*10 + 1 is the smallest prime of form p*10 + 1, where p is a prime.
a(2) = 7 because 701 = 7*100 + 1 is the smallest prime of form p*100 + 1.

Links

Crossrefs

Cf. A121172, A030430, A062800, A007645, A055664, A023203.

Programs

  • Maple
    Primes:= select(isprime,[$1..10^5]):
for n from 1 to 1000 do
   for p in Primes do
      if isprime(p*10^n+1) then
        A[n]:= p
      fi
    od
od:
seq(A[n],n=1..1000); # Robert Israel, May 29 2014
  • Mathematica
    prs=Prime[Range[2000]];Table[i=1;While[!PrimeQ[First[Take[prs,{i}]] 10^n+1],i++];Prime[i],{n,200}] (* Harvey P. Dale, May 15 2011 *)

A120642 Smallest integer k>0 such that k*10^n - 1 is a prime.

Original entry on oeis.org

2, 2, 2, 5, 2, 3, 2, 8, 11, 6, 11, 35, 6, 5, 15, 14, 11, 21, 3, 21, 14, 6, 6, 80, 8, 2, 2, 6, 9, 48, 48, 21, 15, 6, 44, 11, 9, 15, 18, 6, 33, 30, 3, 278, 74, 92, 89, 33, 8, 71, 59, 11, 2, 5, 3, 24, 108, 47, 39, 41, 6, 14, 53, 173, 26, 26, 51, 114, 23, 17, 246, 44, 6, 131, 56, 8, 26, 77, 74
Offset: 1

Views

Author

Jonathan Vos Post, Aug 17 2006

Keywords

Examples

			The primes are 19, 199, 1999, 49999, 199999, 2999999,
19999999, 799999999, 10999999999, 59999999999, ...,.

Links

Crossrefs

Cf. A030430, A037071, A062800, A065582, A121172.

Programs

  • Mathematica
    f[n_] := Block[{k = 1}, While[ !PrimeQ[k*10^n - 1], k++ ]; k]; Array[f, 79] (* Robert G. Wilson v *)

Extensions

a(11) onwards from Robert G. Wilson v, Aug 20 2006

A120729 Smallest integer k>0 such that k*10^n + 1 is a semiprime.

Original entry on oeis.org

3, 2, 2, 5, 1, 1, 1, 1, 1, 2, 4, 2, 3, 7, 4, 3, 6, 6, 4, 1, 2, 4, 13, 2, 4, 3, 7, 21, 6, 9, 3, 1, 5, 4, 16, 19, 28, 19, 9, 3
Offset: 0

Views

Author

Jonathan Vos Post, Aug 17 2006

Keywords

Comments

The corresponding semiprimes are 4, 21, 201, 5001, 10001, 100001, 100001, 10000001, 2000000001, 40000000001, ... Semiprime analog of A121172.

Examples

			a(0) = 3 because 3*10^0 + 1 = 4 = 2^2 is a semiprime.
a(1) = 2 because 2*10^1 + 1 = 21 = 3*7 is a semiprime.
a(2) = 2 because 2*10^2 + 1 = 201 = 3*67 is a semiprime.
a(3) = 5 because 5*10^3 + 1 = 5001 = 3*1667 is a semiprime.
a(4) = 1 because 1*10^4 + 1 = 10001 = 73*137 is a semiprime.
a(5) = 1 because 1*10^5 + 1 = 100001 = 11*9091 is a semiprime.

Crossrefs

Cf. A001358, A030430, A037071, A062800, A065582, A121172.

Programs

  • Mathematica
    sik[n_]:=Module[{k=1,c=10^n},While[PrimeOmega[k*c+1]!=2,k++];k]; Array[sik,40,0] (* Harvey P. Dale, Aug 20 2012 *)

Formula

Smallest integer k>0 such that k*10^n + 1 is in A001358.

Extensions

More terms from Harvey P. Dale, Aug 20 2012
Showing 1-4 of 4 results.

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