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.
a(4)=10111 because 10111 is the smallest prime with four duplicate digits.
Table[ First[ Select[ Prime[ Range[100000]], Max[ DigitCount[ # ]]==i & ]], {i, 6}] (* or *)
f[n_, b_] := Block[{k = 10^(n + 1), p = Permutations[ Join[ Table[ b, {i, 1, n}], {x}]], c = Complement[ Table[j, {j, 0, 9}], {b}], q = {}}, Do[q = Append[q, Replace[p, x -> c[[i]], 2]], {i, 1, 9}]; r = Min[ Select[ FromDigits /@ Flatten[q, 1], PrimeQ[ # ] & ]]; If[ r != Infinity, r, While[ !PrimeQ[k] || Count[ IntegerDigits[k], b] != n, k++ ]; k]]; Table[ f[n, 1], {n, 2, 18}]
A084673(n)=if(n>1,A037055(n),2) \\ M. F. Hasler, Feb 25 2016
Do[a = Table[6, {n}]; k = 0; While[b = FromDigits[ Join[a, IntegerDigits[k] ]]; First[ IntegerDigits[k]] == 6 || !PrimeQ[b], k++ ]; Print[b], {n, 1, 17} ]
a(n) = {if(n==0, return(2)); my(cs = 60*(10^n\9), pow10 = 10); for(i = 1, oo, np = cs; d = 0; while(d < pow10, np = nextprime(np + 1); d = np - cs; if(d < pow10 && digits(d)[1] != 6 || 10*d < pow10, return(np))); cs*=10; pow10*=10)} \\ David A. Corneth, Sep 06 2023
a:= proc(n) local d, h, s;
s:= parse(cat(0, n$n));
for d from 0 do
for h to 10^d-1 do
if isprime(s+h) then return s+h fi
od:
s:= s*10;
od
end:
seq(a(n), n=0..16); # Alois P. Heinz, Feb 11 2021
A088639(n)={ local(p=10^#Str(n),d=1); n*=(p^n-1)/(p-1); until( (d*=10)*(n+1)>p=nextprime(n*d), );p} /* M. F. Hasler, Jan 13 2009 */
from sympy import isprime
def a(n):
if n == 0: return 2
nns, i, pow10 = int(str(n)*n), 1, 1
while True:
i = 1
while i < pow10:
t = nns * pow10 + i
if isprime(t): return t
i += 2
pow10 *= 10
print([a(n) for n in range(16)]) # Michael S. Branicky, Feb 11 2021
a(3)=7 because it is the first prime before 31,59,61,71,73,97,... all remaining prime when 111 is prepended to each of them.
f[n_] := Block[{k = 1, t = Table[1, {n}]}, While[id = IntegerDigits[ Prime[k]]; id[[1]] == 1 || !PrimeQ[ FromDigits[ Join[t, id]]], k++ ]; Prime[k]]; Table[ f[n], {n, 0, 62}] (* Robert G. Wilson v, Apr 09 2005 *)
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