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.
for l from 3 to 31 by 2 do for i from 0 to 9 do for j from 0 to 9 do it1 := sum(i*10^(2*k), k=0..(l-1)/2): it2 := sum(j*10^(2*k+1), k=0..(l-3)/2): if isprime(it1+it2) and i<>j then printf(`%d, `,it1+it2) fi: od: od: od: # James Sellers, Feb 13 2001
t = {}; t1 = {1, 3, 7, 9}; Do[p = 10 a + b; q = 10 b + a; t = Join[t, Select[Table[(p*10^(2 n + 1) - q)/99, {n, 4}], PrimeQ]], {a, t1}, {b, Range[0, 9]}]; Union[t] (* Jayanta Basu, Jun 23 2013 *)
uppQ[n_]:=Module[{idn=IntegerDigits[n]},OddQ[Length[idn]]&& PalindromeQ[ n] && Length[Union[Partition[idn,2]]]==1]; Select[Prime[Range[ 51*10^6]], uppQ] (* or *) Select[FromDigits/@Flatten[Table[Riffle[Table[n,i],k],{n,{1,3,7,9}},{i,5},{k,0,9}],2],#>9&&PrimeQ[#]&]//Sort (* The second program is significantly faster than the first. *) (* Harvey P. Dale, Feb 24 2018 *)
from sympy import isprime A059758_list = [] for l in range(1,300): for a in '1379': for b in '0123456789': if a != b: p = int((a+b)*l+a) if isprime(p): A059758_list.append(p) # Chai Wah Wu, Dec 21 2014
k=11 --> (12*10^11 - 21)/99 = 12121212121.
d[n_]:=IntegerDigits[n]; Length/@d[Select[NestList[FromDigits[Join[d[#],{2,1}]]&,1,1000],PrimeQ]] (* Jayanta Basu, May 25 2013 *)
for(n=1,1e5,ispseudoprime(5^n<<(n+2)\33)&&print1(n",")) \\ M. F. Hasler, Jul 30 2015
k=9 -> (98*10^9 - 89)/99 = 989898989.
extend:= proc(n) local L,j;
L:= convert(n,base,10);
if (L[-1] < L[-2]) xor (nops(L)::odd) then
seq(10*n+j,j=0..L[1]-1)
else
seq(10*n+j,j=L[1]+1..9)
fi
end proc:
und[2]:= [seq(seq(10*i+j,j=subs(i=NULL,[$0..9])),i=1..9)]:
for i from 3 to 4 do und[i]:= map(extend,und[i-1]) od:
select(isprime, [2,3,5,7,seq(op(und[i],i=2..4)]); # Robert Israel, Nov 15 2018
d[n_]:=Differences[IntegerDigits[n]]; mQ[n_]:=MemberQ[d[n],0]==False; a[n_]:=DeleteDuplicates[Sign[Take[d[n],{1,-1,2}]]]; b[n_]:=DeleteDuplicates[Sign[Take[d[n],{2,-1,2}]]]; t={}; Do[p=Prime[n]; If[mQ[p],If[Length[IntegerDigits[p]]<=2,AppendTo[t,p],If[Length[a[p]]==Length[b[p]]==1 && a[p][[1]]!=b[p][[1]],AppendTo[t,p]]]],{n,95}]; t (* Jayanta Basu, May 08 2013 *)
Table[Which[p<10,p,p<100&&Differences[IntegerDigits[p]]!={0},p,p>100&&Union[Total/@ Partition[Sign[Differences[IntegerDigits[p]]],2,1]]=={0},p,True,Nothing],{p,Prime[ Range[ 150]]}] (* Harvey P. Dale, Aug 07 2023 *)
from sympy import isprime
def f(w,dir):
if dir == 1:
for s in w:
for t in range(int(s[-1])+1,10):
yield s+str(t)
else:
for s in w:
for t in range(0,int(s[-1])):
yield s+str(t)
A059168_list = []
for l in range(5):
for d in '123456789':
x = d
for i in range(1,l+1):
x = f(x,(-1)**i)
A059168_list.extend([int(p) for p in x if isprime(int(p))])
if l > 0:
y = d
for i in range(1,l+1):
y = f(y,(-1)**(i+1))
A059168_list.extend([int(p) for p in y if isprime(int(p))]) # Chai Wah Wu, Apr 25 2021
Select[Range[1000], PrimeQ[#] && Length[Union[RealDigits[#][[1]]]] <= 2 &] Select[Prime[Range[200]],Count[DigitCount[#],0]>7&] (* Harvey P. Dale, Jul 14 2017 *)
121 = 11*11 is not prime and thus is not a term of this sequence.
select(isprime,[$0..99,seq(seq(seq(a*(10^(d+1)-10^(d+1 mod 2))/99 + b*(10^d - 10^(d mod 2))/99, b=0..9),a=1..9,2),d=3..9,2)]); # Robert Israel, Jul 08 2016
Select[Union[Flatten[Table[FromDigits[PadRight[{},n,#]],{n,9}]&/@ Tuples[ Range[0,9],2]]],PrimeQ] (* Harvey P. Dale, May 26 2015 *)
from itertools import count, islice
from sympy import isprime, primerange
def agen(): # generator of terms
yield from primerange(2, 100)
yield from (t for t in (int((A+B)*d2+A) for d2 in count(1) for A in "1379" for B in "0123456789") if isprime(t))
print(list(islice(agen(), 51))) # Michael S. Branicky, Jun 09 2022
from sympy import isprime
from itertools import product
def sign(n): return (n > 0) - (n < 0)
def unds(n):
s = str(n)
if len(s) == 1: return True
signs = set(sign(int(s[i-1]) - int(s[i])) for i in range(1, len(s), 2))
if len(signs) > 1: return False
if len(s) % 2 == 0: return signs == {1} or signs == {-1}
return sign(int(s[-1]) - int(s[-2])) in signs - {0}
def candidate_pals(n): # of length 2n + 1
if n == 0: yield from [2, 3, 5, 7]; return # one-digit primes
for rightbutend in product("0123456789", repeat=n-1):
rightbutend = "".join(rightbutend)
for end in "1379": # multi-digit primes must end in 1, 3, 7, or 9
left = end + rightbutend[::-1]
for mid in "0123456789": yield int(left + mid + rightbutend + end)
def a(n): return sum(1 for p in candidate_pals(n) if unds(p) and isprime(p))
print([a(n) for n in range(6)]) # Michael S. Branicky, Apr 15 2021
from sympy import isprime
def f(w,dir):
if dir == 1:
for s in w:
for t in range(int(s[-1])+1,10):
yield s+str(t)
else:
for s in w:
for t in range(0,int(s[-1])):
yield s+str(t)
def A057332(n):
c = 0
for d in '123456789':
x = d
for i in range(1,n+1):
x = f(x,(-1)**i)
c += sum(1 for p in x if isprime(int(p+p[-2::-1])))
if n > 0:
y = d
for i in range(1,n+1):
y = f(y,(-1)**(i+1))
c += sum(1 for p in y if isprime(int(p+p[-2::-1])))
return c # Chai Wah Wu, Apr 25 2021
a[n_]:=DeleteDuplicates[Take[IntegerDigits[n],{1,-1,2}]]; b[n_]:=DeleteDuplicates[Take[IntegerDigits[n],{2,-1,2}]]; t={}; Do[p=Prime[n]; If[p<10, AppendTo[t,p], If[Length[a[p]] == Length[b[p]] == 1 && Abs[a[p][[1]]-b[p][[1]]] == 1, AppendTo[t,p]]], {n,10^5}]; t (* Jayanta Basu, May 08 2013 *)
t1=Join[{2,3,5,7},Select[Range[10,100],PrimeQ[#]&&Abs[Differences[IntegerDigits[#]]]=={1}&]]; Do[a=n*10+(n-1);b=(n-1)*10+n; t1=Join[t1,Select[Table[(a*10^(2*n+1)-b)/99,{n,25}],PrimeQ]]; If[n<=7,c=n*10+(n+1);d=(n+1)*10+n;t1=Join[t1,Select[Table[(c*10^(2*n+1)-d)/99,{n,25}],PrimeQ]]],{n,1,9,2}]; Sort[t1] (* Jayanta Basu, May 09 2013 *)
With[{c=Flatten[{#,Reverse[#]}&/@Table[{a,a+1},{a,0,8}],1]},Flatten[ Select[ Table[ FromDigits[PadRight[{},n,#]],{n,50}],PrimeQ]&/@c]]//Union (* Harvey P. Dale, Aug 20 2022 *)
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