A305352 Deletable primes (A080608) under the stricter rule that leading zeros are disallowed.

2, 3, 5, 7, 13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 103, 107, 113, 127, 131, 137, 139, 157, 163, 167, 173, 179, 193, 197, 223, 229, 233, 239, 263, 269, 271, 283, 293, 307, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 397, 431, 433, 439

Offset

1,1

Comments

Subset of A080608. Numbers 2003, 2017, 2053, 3023, ... are in A080608 but not here.

If you start from a one-digit prime, you can try to build larger and larger deletable primes by inserting digits. If at one point you get stuck and cannot enlarge the number, you have reached a non-insertable prime (A125001). - Jeppe Stig Nielsen, Mar 28 2021

Links

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..10000

Example

2003 is not a member since removing a digit will either give 003 which has a leading zero, or give one of the numbers 203 or 200 which are both composite. However, 2003 is in A080608 because all of 2003, 003, 03, 3 are prime.

Mathematica

Rest@ Union@ Nest[Function[{a, p}, Append[a, With[{w = IntegerDigits[p]}, If[# == True, p, 0] &@ AnyTrue[Array[If[First@ # == 0, 1, FromDigits@ #] &@ Delete[w, #] &, Length@ w], ! FreeQ[a, #] &]]]] @@ {#, Prime[Length@ # + 1]} &, Prime@ Range@ PrimePi@ 10, 81] (* Michael De Vlieger, Aug 02 2018 *)

Prog

(PARI) is(n) = !ispseudoprime(n)&&return(0); my(d=digits(n)); #d==1&&return(1); for(i=1, #d, my(v=vecextract(d, Str("^"i))); v[1]!=0&&is(fromdigits(v))&&return(1)); 0
(Python)
from sympy import isprime
def ok(n):
    if not isprime(n): return False
    if n < 10: return True
    s = str(n)
    si = (s[:i]+s[i+1:] for i in range(len(s)))
    return any(t[0] != '0' and ok(int(t)) for t in si)
print([k for k in range(440) if ok(k)]) # Michael S. Branicky, Jan 28 2023

Crossrefs

Cf. A080608, A080603, A096235-A096246, A125001, A322474.

Sequence in context: A234851 A179336 A080608 * A347864 A137812 A216578

Adjacent sequences: A305349 A305350 A305351 * A305353 A305354 A305355

Keyword

nonn,base

Author

Jeppe Stig Nielsen, Aug 01 2018

Status

approved