cp's OEIS Frontend

A034895 Dropping any digit gives a prime number.

%I A034895 #52 May 22 2025 10:20:06
%S A034895 22,23,25,27,32,33,35,37,52,53,55,57,72,73,75,77,111,113,117,119,131,
%T A034895 137,171,173,179,197,311,317,371,411,413,417,431,437,471,473,611,617,
%U A034895 671,711,713,719,731,1013,1031,1037,1073,1079,1097,1379,1397,1499,1673
%N A034895 Dropping any digit gives a prime number.
%C A034895 The prime terms are in A051362.
%C A034895 The number of terms < 10^n: 0, 16, 43, 101, 159, 267, 350, 476, 582, 751, ..., . - _Robert G. Wilson v_, Oct 09 2014
%C A034895 Includes 10*x+1 for x in A004022. - _Robert Israel_, Jan 14 2016
%H A034895 Robert G. Wilson v, <a href="/A034895/b034895.txt">Table of n, a(n) for n = 1..752</a> (first 485 terms from T. D. Noe)
%e A034895 1379 is in the sequence since 379, 179, 139 & 137 are all primes. - _Robert G. Wilson v_, Oct 07 2014
%t A034895 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 *)
%t A034895 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 *)
%o A034895 (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
%o A034895 (PARI) DroppingAnyDigitGivesAPrime(N,b) = {
%o A034895 \\ Property-testing function; returns 1 if true for N, 0 otherwise
%o A034895 \\ Works with any base b. Here usable with b=10.
%o A034895   my(k=b,m); if(N<b,return(0));
%o A034895   while(N>=(k\b), m=(N\k)*(k\b)+(N%(k\b));
%o A034895     if ((m<2)||(!isprime(m)),return(0)); k*=b);
%o A034895   return(1);
%o A034895 } \\ _Stanislav Sykora_, Jan 14 2016
%o A034895 (Python) from sympy import isprime
%o A034895 def is_A034895(n):
%o A034895     s = str(n)
%o A034895     return n>9 and all(isprime(int(s[:i]+s[i+1:])) for i in range(len(s)))
%o A034895 # _David Radcliffe_, Dec 11 2017
%Y A034895 Cf. A267413.
%K A034895 nonn,base,nice
%O A034895 1,1
%A A034895 _Erich Friedman_