A070854 -id:A070854 - cp's OEIS frontend

A121172 Smallest integer k>0 such that k*10^n + 1 is a prime.

1, 1, 3, 7, 7, 22, 3, 6, 6, 3, 19, 18, 4, 39, 6, 13, 37, 15, 15, 6, 16, 9, 96, 61, 19, 6, 9, 3, 33, 63, 57, 117, 55, 49, 30, 3, 28, 6, 42, 24, 36, 72, 21, 60, 6, 24, 33, 61, 21, 85, 31, 49, 13, 93, 18, 90, 9, 16, 135, 19, 55, 9, 135, 60, 6, 30, 3, 16, 115, 114, 19, 99, 15, 147, 171, 42

Offset: 1

Alexander Adamchuk, Aug 14 2006

nonn

			a(1) = 1 because A030430[1] = 11 is a smallest prime of form 10*k + 1.
a(2) = 1 because A062800[1] = 101 is a smallest prime of form 100*k + 1.

Robert Price, Table of n, a(n) for n = 1..1000

Cf. A030430, A062800, see A070854 for resulting primes.

s={};Do[k=0;Until[PrimeQ[k*10^n+1],k++];AppendTo[s,k],{n,76}];s (* James C. McMahon, Oct 13 2024 *)

a(n) = (A070854(n)-1)/10^n. - Ray Chandler, Feb 10 2009

Minor edits by Ray Chandler, Feb 10 2009

A379150 Smallest prime ending in "3", with n preceding "0" digits.

Original entry on oeis.org

103, 2003, 70003, 100003, 1000003, 20000003, 500000003, 40000000003, 40000000003, 100000000003, 2000000000003, 230000000000003, 3100000000000003, 11000000000000003, 20000000000000003, 100000000000000003, 1000000000000000003, 310000000000000000003, 500000000000000000003

Offset: 1

James S. DeArmon, Dec 16 2024

Leading zeros are not allowed, e.g., "03".

a(997) has 1001 digits. - Michael S. Branicky, Dec 16 2024

			a(1) = 103, is the smallest prime ending in "03";
a(2) = 2003, is the smallest prime ending in "003".

Michael S. Branicky, Table of n, a(n) for n = 1..996

Cf. A070854, A070847.

Table[i=1;While[!PrimeQ[m=FromDigits[Join[IntegerDigits[i],Table[0,n],{3}]]],i++];m,{n,19}] (* James C. McMahon, Dec 23 2024 *)

a(n)=for(i=1, oo, if(isprime(i*10^(n+1)+3), return(i*10^(n+1)+3))) \\ Johann Peters, Dec 27 2024

import sympy
def prime3_finder():
  outVec = []
  power = 2
  for n in range(100,999999999):
      if not n & 3 == 3: continue # speed-up over simple MOD operation
      if not n % 10**power == 3: continue
      if not sympy.isprime(n): continue
      outVec.append(n)
      power += 1
  return outVec
outvec = prime3_finder()
print(outvec)

from sympy import isprime
from itertools import count
def a(n): return next(i for i in count(10**(n+1)+3, 10**(n+1)) if isprime(i))
print([a(n) for n in range(1, 20)]) # Michael S. Branicky, Dec 16 2024

More terms from Michael S. Branicky, Dec 16 2024

cp's OEIS Frontend

A121172 Smallest integer k>0 such that k*10^n + 1 is a prime.

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