cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A034302 Zeroless primes that remain prime if any digit is deleted.

Original entry on oeis.org

23, 37, 53, 73, 113, 131, 137, 173, 179, 197, 311, 317, 431, 617, 719, 1499, 1997, 2239, 2293, 3137, 4919, 6173, 7433, 9677, 19973, 23833, 26833, 47933, 73331, 74177, 91733, 93491, 94397, 111731, 166931, 333911, 355933, 477797, 477977
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A034303, A034304, A034305, A051362, A010051, A038618.

Programs

  • Haskell
    import Data.List (inits, tails)
a034302 n = a034302_list !! (n-1)
a034302_list = filter f $ drop 4 a038618_list where
   f x = all (== 1) $ map (a010051 . read) $
             zipWith (++) (inits $ show x) (tail $ tails $ show x)
-- Reinhard Zumkeller, Dec 17 2011
  • Mathematica
    rpnzQ[n_]:=Module[{idn=IntegerDigits[n]},Count[idn,0]==0 && And@@ PrimeQ[FromDigits/@ Subsets[IntegerDigits[n], {Length[idn]-1}]]]; Select[Prime[Range[40000]],rpnzQ]  (* Harvey P. Dale, Mar 24 2011 *)
  • PARI
    is(n)=my(d=digits(n),t=2^#d-1); if(vecmin(d)==0, return(0)); for(i=0,#d-1, if(!isprime(fromdigits(vecextract(d,t-2^i))), return(0))); isprime(n) \\ Charles R Greathouse IV, Jun 23 2017
  • Python
    from itertools import product
from sympy import isprime
A034302_list, m = [23, 37, 53, 73], 7
for l in range(1,m-1): # generate all terms less than 10^m
    for d in product('123456789',repeat=l):
        for e in product('1379',repeat=2):
            s = ''.join(d+e)
            if isprime(int(s)):
                for i in range(len(s)):
                    if not isprime(int(s[:i]+s[i+1:])):
                        break
                else:
                    A034302_list.append(int(s)) # Chai Wah Wu, Apr 05 2021

A034305 Zeroless nonprimes that remain nonprime if any digit is deleted.

Original entry on oeis.org

14, 16, 18, 44, 46, 48, 49, 64, 66, 68, 69, 81, 84, 86, 88, 91, 94, 96, 98, 99, 122, 124, 125, 126, 128, 142, 144, 145, 146, 148, 152, 154, 155, 156, 158, 162, 164, 165, 166, 168, 182, 184, 185, 186, 188, 212, 214, 215, 216, 218, 221, 222, 224, 225, 226, 228
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Subsequence of A052382.
Cf. A034302, A034303, A034304, A010051.

Programs

  • Haskell
    a034305 n = a034305_list !! (n-1)
a034305_list = filter f $ drop 9 a052382_list where
  f x = a010051' x == 0 &&
        (all (== 0) $ map (a010051' . read) $
         zipWith (++) (inits $ show x) (tail $ tails $ show x))
-- Reinhard Zumkeller, May 10 2015
  • Mathematica
    npQ[n_]:=!PrimeQ[n]&&FreeQ[IntegerDigits[n],0]&&AllTrue[FromDigits/@ Table[Drop[IntegerDigits[n],{k}],{k,IntegerLength[n]}],!PrimeQ[#]&]; Select[Range[10,300],npQ](* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 19 2021 *)
  • PARI
    is(n)=my(d=digits(n)); if(#d<2 || vecmin(d)<1 || isprime(n), return(0)); for(i=0,#d-1, if(isprime(fromdigits(vecextract(d,2^#d-1-2^i))), return(0))); 1 \\ Charles R Greathouse IV, Jun 25 2017
  • Python
    from sympy import isprime
def ok(n):
    if n < 10 or isprime(n): return False
    s = str(n)
    return "0" not in s and not any(isprime(int(s[:i]+s[i+1:])) for i in range(len(s)))
print([k for k in range(229) if ok(k)]) # Michael S. Branicky, Jan 15 2023

Extensions

Definition corrected by T. D. Noe, Apr 02 2008
Single-digit terms removed again by Georg Fischer, Jun 21 2021

A057877 a(n) = smallest n-digit prime in A057876.

Original entry on oeis.org

23, 113, 1531, 12239, 111317, 1111219, 11119291, 111111197, 1111113173, 11111133017, 111111189919, 1111111411337, 11111111161177, 111111111263311, 1111111111149119, 11111111111179913, 111111111111118771, 1111111111111751371, 11111111111111111131, 111111111111113129773, 1111111111111111337111
Offset: 2

Views

Author

Patrick De Geest, Oct 15 2000

Keywords

Examples

			1531 gives primes 53, 131 and 151 after dropping digits 1, 5 and 3.

Crossrefs

Cf. A057876, A057877, A057878, A057879, A057880, A057881, A057882, A057883, A051362, A034302, A034303, A034304, A034305.

Programs

  • Maple
    filter:= proc(n) local L,d,Lp;
  if not isprime(n) then return false fi;
  L:= convert(n,base,10);
  for d in convert(L,set) do
    Lp:= subs(d=NULL,L);
    if Lp=[] or Lp[-1] = 0 then return false fi;
    if not isprime(add(Lp[i]*10^(i-1),i=1..nops(Lp))) then return false fi;
  od;
  true
end proc:
Res:= NULL:
for t from 1 to 21 do
  for x from (10^(t+1)-1)/9 by 2 do
    if filter(x) then Res:= Res, x; break fi
  od
od:
Res; # Robert Israel, Jul 13 2018
  • Mathematica
    Do[k = (10^n - 1)/9; While[d = IntegerDigits[k]; !PrimeQ[k] || !PrimeQ[ FromDigits[ DeleteCases[d, 0]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 1]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 2]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 3]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 4]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 5]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 6]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 7]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 8]]] || !PrimeQ[ FromDigits[ DeleteCases[d, 9]]], k++ ]; Print[k], {n, 2, 19}]

Extensions

Extended by Robert G. Wilson v, Dec 17 2002
More terms from Robert Israel, Jul 13 2018
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.