A099664
a(n) is the largest prime before A002278(n).
Original entry on oeis.org
3, 43, 443, 4441, 44417, 444443, 4444409, 44444399, 444444443, 4444444429, 44444444441, 444444444443, 4444444444439, 44444444444353, 444444444444421, 4444444444444423, 44444444444444411, 444444444444444419
Offset: 1
A200065
Start with n, concatenate its trivial divisors, and repeat until a prime is reached. a(n) = 0 if no prime is ever reached.
Original entry on oeis.org
0, 0, 13, 0, 0, 0, 17, 0, 19, 0, 1111111111111111111, 0, 113, 0, 0, 0, 1117, 0, 11119, 0, 111121, 0, 1123, 0, 0, 0, 127, 0, 1129, 0, 131, 0
Offset: 1
17 -> {1, 17} = 117 (composite) -> {1, 117} = 1117 (prime), so a(17) = 1117.
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lst = {}; Do[If[DivisorSigma[0, n] == 1 || Divisible[n, 5] || EvenQ[n], AppendTo[lst, 0], If[PrimeQ[n], n = 10^Length[IntegerDigits[n]] + n]; While[True, If[PrimeQ[n], Break[]]; n = FromDigits[Flatten[IntegerDigits[{1, n}]]]]; AppendTo[lst, n]], {n, 32}]; lst
A384873
a(n) is the smallest n-digit zeroless prime.
Original entry on oeis.org
2, 11, 113, 1117, 11113, 111119, 1111151, 11111117, 111111113, 1111111121, 11111111113, 111111111149, 1111111111139, 11111111111123, 111111111111229, 1111111111111123, 11111111111111119, 111111111111111131, 1111111111111111111, 11111111111111111131
Offset: 1
The list of 3-digit prime numbers starts with 101, 103, 107, 109, and 113. Among these, 113 is the first that does not contain the digit 0. So, a(3) = 113.
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f:= proc(n) local x;
for x from (10^n-1)/9 by 2 do
if isprime(x) and not member(0,convert(x,base,10)) then return x fi
od
end proc:
f(1):= 2:
map(f, [$1..20]); # Robert Israel, Jun 12 2025
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a[n_]:=Module[{k=PrimePi[10^n/9-1]},Until[DigitCount[Prime[k],10,0]==0,k++];Prime[k]] (* James C. McMahon, Jun 21 2025 *)
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a(n) = forprime(p=(10^n-1)/9, , if (vecmin(digits(p)), return(p))); \\ Michel Marcus, Jun 15 2025
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from itertools import product
from sympy import isprime
def a(n):
for t in product('123456789', repeat=n):
p = int(''.join(t))
if isprime(p): return p
print([a(n) for n in range(1, 21)])
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from sympy import nextprime
def A384873(n):
m = nextprime((10**n-1)//9-1)
while '0' in str(m):
m = nextprime(m)
return m # Chai Wah Wu, Jun 20 2025
A099657
a(n) is the least prime following A002277(n) repdigits.
Original entry on oeis.org
2, 5, 37, 337, 3343, 33343, 333337, 3333373, 33333347, 333333349, 3333333403, 33333333343, 333333333367, 3333333333347, 33333333333437, 333333333333389, 3333333333333343, 33333333333333391, 333333333333333391
Offset: 0
n=3: 33 is followed by 37.
A099661
a(n) is the least prime following A002281(n) repdigits.
Original entry on oeis.org
2, 11, 79, 787, 7789, 77783, 777781, 7777801, 77777803, 777777799, 7777777781, 77777777827, 777777777841, 7777777777859, 77777777777837, 777777777777787, 7777777777777867, 77777777777777797, 777777777777777817
Offset: 0
n=6: 77 is followed by 79.
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Table[NextPrime[7*(10^n-1)/9], {n, 0, 35}]
NextPrime/@LinearRecurrence[{11,-10},{0,7},35] (* Harvey P. Dale, Dec 12 2021 *)
A099663
a(n) is the largest prime before A002276(n).
Original entry on oeis.org
19, 211, 2221, 22193, 222199, 2222219, 22222199, 222222193, 2222222137, 22222222189, 222222222169, 2222222222197, 22222222222201, 222222222222151, 2222222222222203, 22222222222222153, 222222222222222221, 2222222222222222177, 22222222222222222169, 222222222222222222149, 2222222222222222222161
Offset: 2
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Table[NextPrime[2(10^n-1)/9, -1], {n, 2, 35}]
Drop[NextPrime[#,-1]&/@LinearRecurrence[{11,-10},{0,2},20],2] (* Harvey P. Dale, Dec 19 2020 *)
A099665
a(n) is the largest prime before A002279(n).
Original entry on oeis.org
3, 53, 547, 5531, 55547, 555523, 5555527, 55555553, 555555541, 5555555519, 55555555543, 555555555551, 5555555555551, 55555555555541, 555555555555529, 5555555555555539, 55555555555555519, 555555555555555487, 5555555555555555533, 55555555555555555483, 555555555555555555491
Offset: 1
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Table[NextPrime[5*(10^n-1)/9, -1], {n, 1, 35}]
NextPrime[#,-1]&/@Table[FromDigits[PadRight[{},n,5]],{n,20}] (* Harvey P. Dale, Aug 31 2015 *)
A099666
a[n] is the largest prime before A002280[n] repdigits.
Original entry on oeis.org
5, 61, 661, 6661, 66653, 666649, 6666617, 66666653, 666666653, 6666666661, 66666666643, 666666666619, 6666666666629, 66666666666647, 666666666666647, 6666666666666571, 66666666666666601, 666666666666666661
Offset: 1
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