A020457 -id:A020457 - cp's OEIS frontend

A154981 Primes with nonprime smallest digit.

11, 13, 17, 19, 31, 41, 47, 61, 67, 71, 89, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 241, 251, 271, 281, 307, 311, 313, 317, 331, 401, 409, 419, 421, 431, 449, 457, 461, 467, 479, 487, 491

Offset: 1

Juri-Stepan Gerasimov, Jan 19 2009

Nonprime digits in base 10 are 0, 1, 4, 6, 8 and 9.

			17 is in the sequence because its smallest digit is 1, which is not prime.
19 is in the sequence because its smallest digit is 1, which is not prime (neither is 9, for that matter).
23 is not in the sequence because both of its digits are prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A019546, A020457, A141468.

Select[Prime[Range[150]], Not[PrimeQ[Min[IntegerDigits[#]]]] &] (* Alonso del Arte, Mar 28 2014, based on Harvey P. Dale's program for A155053 *)

Entries checked by R. J. Mathar, Mar 29 2010

A036936 Smallest n-digit prime containing only digits 1 and 9, or 0 if no such prime exists.

Original entry on oeis.org

0, 11, 191, 1999, 11119, 111119, 1111991, 11111119, 111111199, 1111111919, 11111111911, 111111199919, 1111111119919, 11111111119111, 111111111119119, 1111111111111999, 11111111111111119, 111111111111191111

Offset: 1

Patrick De Geest, Jan 04 1999

Jinyuan Wang, Table of n, a(n) for n = 1..500

Cf. A020457, A036229, A036309.

Table[SelectFirst[FromDigits/@Tuples[{1,9},n],PrimeQ],{n,20}]/. Missing["NotFound"]->0 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 26 2020 *)

A386004 Primes whose digit set intersects the odd digits in at most one element and intersects the even digits in at most two elements.

Original entry on oeis.org

2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 181, 211, 223, 227, 229, 233, 241, 263, 269, 277, 281, 283, 383, 401, 409, 421, 433, 443, 449, 461, 463, 467, 487, 499, 601, 607, 641, 643, 647, 661, 677, 683, 727, 787, 809, 811, 821, 823, 827, 829, 863

Offset: 1

Jean-Marc Rebert, Jul 14 2025

From David A. Corneth, Jul 14 2025: (Start)
Terms can have at most three distinct digits.
Terms > 5 cannot have a digit 5. Proof: Terms > 5 are odd as they are prime. They cannot have a last digit 5. So if they have a digit 5 then they have at least two distinct odd digits contradicting the sequence definition of having at most one odd digit. (End)

			101 is a term because it is prime and its digit set is {0, 1} — containing at most one odd digit and no more than two distinct even digits.
1021 is a term because it is prime and its digit set is {0,1,2} — containing at most one odd digit and no more than two distinct even digits.

Cf. A000040, A020469, A020450, A020457, A020460, A385770.

Select[Prime[Range[150]],Length[Intersection[d=IntegerDigits[#],{1,3,5,7,9}]]<=1 && Length[Intersection[d,{0,2,4,6,8}]]<=2 &] (* Stefano Spezia, Jul 14 2025 *)

is(n) = if(!isprime(n), return(0)); my(s=Set(digits(n)), odd=0); if(#s>3,return(0)); odd=sum(i=1, #s ,bitand(s[i], 1)); if(odd > 1, return(0)); if(#s-odd > 2, return(0)); 1 \\ David A. Corneth, Jul 14 2025

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A154981 Primes with nonprime smallest digit.

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A036936 Smallest n-digit prime containing only digits 1 and 9, or 0 if no such prime exists.

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A386004 Primes whose digit set intersects the odd digits in at most one element and intersects the even digits in at most two elements.

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