A034895 Dropping any digit gives a prime number.

22, 23, 25, 27, 32, 33, 35, 37, 52, 53, 55, 57, 72, 73, 75, 77, 111, 113, 117, 119, 131, 137, 171, 173, 179, 197, 311, 317, 371, 411, 413, 417, 431, 437, 471, 473, 611, 617, 671, 711, 713, 719, 731, 1013, 1031, 1037, 1073, 1079, 1097, 1379, 1397, 1499, 1673

Offset: 1

Author

Erich Friedman

Keywords

• nonn
• base
• nice

Comments

The prime terms are in A051362.

The number of terms < 10^n: 0, 16, 43, 101, 159, 267, 350, 476, 582, 751, ..., . - Robert G. Wilson v, Oct 09 2014

Includes 10*x+1 for x in A004022. - Robert Israel, Jan 14 2016

Examples

			1379 is in the sequence since 379, 179, 139 & 137 are all primes. - _Robert G. Wilson v_, Oct 07 2014
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..752 (first 485 terms from T. D. Noe)

Crossrefs

Cf. A267413.

Programs

Mathematica

fQ[n_] := Union[ PrimeQ[ Table[ Quotient[n, 10^k]*10^(k - 1) + Mod[n, 10^(k - 1)], {k, 1 + Floor@ Log10@ n}] ]] == {True}; Select[ Range@ 1675, fQ] (* Robert G. Wilson v, Oct 07 2014 *)
ddpnQ[n_]:=With[{id=IntegerDigits[n]},AllTrue[Table[FromDigits[Drop[id,{i}]],{i,Length[id]}],PrimeQ]]; Select[Range[2000],ddpnQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 12 2017 *)

PARI

isok(n) = {d = digits(n); for (i=1, #d, nd = []; for (k=1, #d, if (k != i, nd = concat(nd, d[k]));); if (! isprime(subst(Pol(nd), x, 10)), return (0));); return (1);} \\ Michel Marcus, Jul 17 2014

PARI

DroppingAnyDigitGivesAPrime(N,b) = {
\\ Property-testing function; returns 1 if true for N, 0 otherwise
\\ Works with any base b. Here usable with b=10.
  my(k=b,m); if(N=(k\b), m=(N\k)*(k\b)+(N%(k\b));
    if ((m<2)||(!isprime(m)),return(0)); k*=b);
  return(1);
} \\ Stanislav Sykora, Jan 14 2016

Python

from sympy import isprime
def is_A034895(n):
    s = str(n)
    return n>9 and all(isprime(int(s[:i]+s[i+1:])) for i in range(len(s)))
# David Radcliffe, Dec 11 2017