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.
16169191 is a term because it is equal to 101 * 160091.
9887 is prime, 9887 = 9886+1 and 9886 turned upside-down is 9886 again.
lst = {}; fQ[n_] := Block[{allset = {0, 1, 6, 8, 9}, id = IntegerDigits@n}, Union@ Join[id, allset] == allset && Reverse[id /. {6 -> 9, 9 -> 6}] == id]; Do[ If[ PrimeQ@n && fQ@n, AppendTo[lst, n]], {n, 2000000}]; lst (* Robert G. Wilson v, Feb 27 2007 *)
from sympy import isprime
from itertools import count, islice, product
def ud(s): return s[::-1].translate({ord('6'):ord('9'), ord('9'):ord('6')})
def agen():
for d in count(2):
for start in "1689":
for rest in product("01689", repeat=d//2-1):
left = start + "".join(rest)
right = ud(left)
for mid in [[""], ["0", "1", "8"]][d%2]:
t = int(left + mid + right)
if isprime(t):
yield t
print(list(islice(agen(), 33))) # Michael S. Branicky, Mar 29 2022
is_A045574(n)=n%10 & !setminus(Set(Vec(Str(n))),Vec("01689")) || !n \\ M. F. Hasler, May 04 2012
compdig := proc(n) if(n=2)then return 5: elif(n=5)then return 2: elif(n=0 or n=1 or n=8)then return n: else return -1: fi: end: isA053701 := proc(n) local d,l,j: d:=convert(n,base,10): l:=nops(d): for j from 1 to ceil(l/2) do if(not d[j]=compdig(d[l-j+1]))then return false: fi: od: return true: end: for n from 0 to 10000 do if(isA053701(n))then printf("%d, ",n): fi: od: # Nathaniel Johnston, May 17 2011
from itertools import count, islice, product
def lr(s): return s[::-1].translate({ord('2'):ord('5'), ord('5'):ord('2')})
def A053701gen(): # generator of terms
yield from [0, 1, 8]
for d in count(2):
for first in "1258":
for rest in product("01258", repeat=d//2-1):
left = first + "".join(rest)
for mid in [[""], ["0", "1", "8"]][d%2]:
yield int(left + mid + lr(left))
print(list(islice(A053701gen(), 45))) # Michael S. Branicky, Jul 09 2022
NextPalindrome[n_] := Block[{l = Floor[Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[idn, Ceiling[l/2]]]] > FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[idn, Ceiling[l/2]], Reverse[ Take[idn, Floor[l/2]]]]], idfhn = FromDigits[ Take[idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[ idfhn], Drop[ Reverse[ IntegerDigits[ idfhn]], Mod[l, 2]]]]]]]]; np = 0; t = {0}; Do[np = NextPalindrome[np]; If[Union[Join[{0, 1, 8}, IntegerDigits[np]]] == {0, 1, 8}, AppendTo[t, np]], {n, 1150}]; t (* Robert G. Wilson v *)
TetrNumsUpTo10powerK[k_]:= Select[FromDigits/@ Tuples[{0, 1, 8}, k],IntegerDigits[#] == Reverse[IntegerDigits[#]] &]; TetrNumsUpTo10powerK[7] (* Mikk Heidemaa, May 21 2017 *)
{for(l=1,5,u=vector((l+1)\2,i,10^(i-1)+(2*i-11&&i==1,2]), print1((v+v\2*6)*u", ")))} \\ The n-th term could be produced by using (partial sums of) A225367 to skip all shorter terms, and then skipping the adequate number of vectors v until n is reached. - M. F. Hasler, May 05 2013
from itertools import count, islice, product
def agen():
yield from [0, 1, 8]
for d in count(2):
for start in "18":
for rest in product("018", repeat=d//2-1):
left = start + "".join(rest)
for mid in [[""], ["0", "1", "8"]][d%2]:
yield int(left + mid + left[::-1])
print(list(islice(agen(), 42))) # Michael S. Branicky, Mar 29 2022
1680891 is a member because it is the same upside down (A000787) and also a cyclops number (A134808).
Select[Range[10^7], And[OddQ@ Length@#, Part[#, Ceiling[Length[#]/2]] == 0, Times @@ Boole@ Map[MemberQ[{0, 1, 6, 8, 9}, #] &, Union@ #] == 1, Count[#, 0] == 1, (Take[#, Floor[Length[#]/2]] /. {6 -> 9, 9 -> 6}) ==
Reverse@ Take[#, -Floor[Length[#]/2]]] &@ IntegerDigits@ # &] (* Michael De Vlieger, Jul 05 2016 *)
import sys
f = open('b153806.txt', 'w')
i = 1
n = 0
a = [""]
r = [""] #reversed strobogrammatically
while True:
for x,y in zip(a,r):
f.write(str(i)+" "+x+"0"+y+"\n")
i += 1
if i>20000:
f.close()
sys.exit()
a = sum([[x+"1",x+"6",x+"8",x+"9"] for x in a],[])
r = sum([["1"+x,"9"+x,"8"+x,"6"+x] for x in r],[])
# Kenny Lau, Jul 05 2016
Select[FromDigits/@Tuples[{0,1,6,8 , 9},4],PrimeQ] (* Harvey P. Dale, Oct 24 2015 *)
main=print$"0":concat[concat[[reverse(reverse(map f x)++z++x)|x<-y]|z<-["","0"]]|y<-s(iterate i"6")];f '0'='0';f '6'='9';f '9'='6';i('0':x)='6':x;i('6':x)='9':x;i('9':x)='0':i x;i""="6";s(x:y@(z:_))=let w:v=s y in if length x==length z then(x:w):v else[x]:w:v
fQ[n_] := Block[{s = {0, 6, 9}, id = IntegerDigits[n]}, If[ Union[ Join[s, id]] == s && (id /. {6 -> 9, 9 -> 6}) == Reverse[id], True, False]]; Select[ Range[0, 10^6], fQ[ # ] &] (* Robert G. Wilson v, Oct 11 2005 *)
is_A111065(n)=!setminus(Set(n=Vec(Str(n))),Vec("069")) & apply(t->Vec("096")[max(eval(t)/3,1)], n)==vecextract(n,"-1..1") \\ M. F. Hasler, May 04 2012
from itertools import count, islice, product
def ud(s): return s[::-1].translate({ord('6'):ord('9'), ord('9'):ord('6')})
def agen():
yield 0
for d in count(2):
for start in "69":
for rest in product("069", repeat=d//2-1):
left = start + "".join(rest)
right = ud(left)
for mid in [[""], ["0"]][d%2]:
yield int(left + mid + right)
print(list(islice(agen(), 37))) # Michael S. Branicky, Mar 29 2022
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