A319596 Base-3 deletable primes (written in base 10).

2, 5, 7, 11, 17, 19, 23, 29, 47, 53, 59, 61, 71, 73, 83, 89, 101, 107, 137, 167, 173, 179, 181, 191, 197, 223, 233, 251, 263, 269, 317, 431, 461, 491, 503, 509, 521, 541, 547, 557, 569, 587, 593, 653, 659, 673, 677, 683, 701, 709, 719, 809, 911, 947, 953

Offset

1,1

Comments

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (first 177 terms from Robert Price)

Maple

S:= {2}: count:= 0:
p:= 2;
while count < 200 do
  p:= nextprime(p);
  d:= floor(log[3](p));
  for i from 0 to d do
    x:= p mod 3^(i+1);
    q:= (x mod 3^i) + (p-x)/3;
    if q >= 3^(d-1) and member(q, S) then
       S:= S union {p}; count:= count+1; break
      fi
  od;
od:
sort(convert(S, list)); # Robert Israel, Nov 26 2020

Mathematica

b = 3; d = {};
p = Select[Range[2, 10000], PrimeQ[#] &];
For[i = 1, i <= Length[p], i++,
  c = IntegerDigits[p[[i]], b];
  If[Length[c] == 1, AppendTo[d, p[[i]]]; Continue[]];
  For[j = 1, j <= Length[c], j++,
   t = Delete[c, j];
   If[t[[1]] == 0, Continue[]];
   If[MemberQ[d, FromDigits[t, b]], AppendTo[d, p[[i]]]; Break[]]]];
d (* Robert Price, Dec 05 2018 *)

Prog

(Python)
from sympy import isprime
from sympy.ntheory.digits import digits
def ok(n, base=3):
    if not isprime(n): return False
    if n < 3: return True
    s = "".join(str(d) for d in digits(n, base)[1:])
    si = (s[:i]+s[i+1:] for i in range(len(s)))
    return any(t[0] != '0' and ok(int(t, base)) for t in si)
print([k for k in range(954) if ok(k)]) # Michael S. Branicky, Jan 14 2022

Crossrefs

Cf. A080608, A080603, A096235-A096246.

Sequence in context: A023238 A194991 A345667 * A235480 A049042 A020605

Adjacent sequences: A319593 A319594 A319595 * A319597 A319598 A319599

Keyword

nonn,base,easy

Author

Robert Price, Nov 14 2018

Extensions

Removed the term 3. As pointed out by Kevin Ryde, there is no need to "seed" the list using base-2 assumptions. - Robert Price, Dec 05 2018

Status

approved