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.
11, 113, 11311, etc. are primes.
11, 11777, 1177711, ... are all prime.
3, 37, 373, 373777, ... are all prime.
id[n_]:=IntegerDigits[n]; f[x_,y_]:=FromDigits[Flatten[Append[{x},y]]]; a[x_,y_]:=NestWhile[f[id[#],y]&,f[id[x],y],!PrimeQ[#]&]; d[x_, y_]:=x-FromDigits[PadRight[id[y],Length[id[x]]]]; t={3}; x=3; Do[y=a[x,7]; AppendTo[t,d[y,x]]; x=a[y,3]; AppendTo[t,d[x,y]],{n,4}]; t (* Jayanta Basu, May 20 2013 *)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
s = ""
while True:
for d in "13":
for k in count(1):
if isprime(int(s+d*k)): break
yield k
s += d*k
print(list(islice(agen(), 10))) # Michael S. Branicky, Aug 23 2022
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
s = ""
while True:
for d in "17":
for k in count(1):
if isprime(int(s+d*k)): break
yield k
s += d*k
print(list(islice(agen(), 11))) # Michael S. Branicky, Aug 23 2022
I:=[4,49,144,9,324,42849]; [n le 6 select I[n] else 9*(Self(n-2) - 27*Self(n-4) +2187*Self(n-6)): n in [1..31]]; // G. C. Greubel, Jan 12 2022
a[n_]:= With[{p=Sqrt[27]}, Simplify[(p^n/12)*(9*((2+p) + (-1)^n*(2-p)) + (49 - 37*(-1)^n)*ChebyshevU[n, 3/p] -(153-261*(-1)^n)/p*ChebyshevU[n-1, 3/p] )]];
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Jan 12 2022 *)
Vec((4 + 49*x + 108*x^2 - 432*x^3 + 54675*x^5) / ((1 - 6*x + 27*x^2)*(1 - 27*x^2)*(1 + 6*x + 27*x^2)) + O(x^20)) \\ Colin Barker, May 06 2019
U=chebyshev_U p=sqrt(27) def A112533(n): return (p^n/12)*( 9*((2+p) + (-1)^n*(2-p)) + (49 - 37*(-1)^n)*U(n, 3/p) - (1/p)*(153 - 261*(-1)^n)*U(n-1, 3/p) ) [A112533(n) for n in (0..30)] # G. C. Greubel, Jan 12 2022
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