A020450 -id:A020450 - cp's OEIS frontend

A334170 Emirps containing only the digits 1 and 2.

111211, 112111, 12122221, 12222121, 1111122121, 1212211111, 11121211121, 11212221121, 12111212111, 12112221211, 111122221121, 111122222111, 111122222221, 111211221221, 111212212211, 111212222111, 111222212111, 111222221111, 112111211221, 112122112211, 112122211121

Offset: 1

Daniel Starodubtsev, Apr 17 2020

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Intersection of A007931 and A006567.

Subsequence of A020450.

Union @ Flatten @ Table[FromDigits /@ Select[Tuples[{1, 2}, n] ,PrimeQ @ (m = FromDigits[#]) && # != (r = Reverse[#]) && PrimeQ @ FromDigits[r] &], {n, 12}] (* Amiram Eldar, Apr 18 2020 *)
Table[Select[FromDigits/@Tuples[{1,2},n],!PalindromeQ[#]&&AllTrue[ {#,IntegerReverse[ #]},PrimeQ]&],{n,12}]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 08 2020 *)

isok(p) = if (isprime(p), my(d=digits(p), rd=Vecrev(d)); (vecsort(d,,8) == [1,2]) && isprime(fromdigits(rd)) && (rd != d));
lista(nn) = {for (n=1, nn, my(vf = vector(n, k, 1)); for (i=1, 2^n-1, my(vpos = select(x->(x==1), Vecrev(binary(i)), 1), nvf = vf); for (i=1, #vpos, nvf[vpos[i]] = 2;); my(x = eval(Str(1, fromdigits(Vecrev(nvf)), 1))); if (isok(x), print1(x, ", "));););} \\ Michel Marcus, Apr 18 2020

A276461 Prime numbers whose digits are k+1 1's and k 2's for some k >= 1.

Original entry on oeis.org

211, 12211, 21121, 21211, 22111, 1121221, 1212121, 2121121, 2211211, 2221111, 111221221, 112212211, 112221211, 121211221, 211122211, 211212121, 211222111, 221112121, 221212111, 11122121221, 11122221211, 11211221221, 11212211221, 11212221121, 11222112211

Offset: 1

Bob Selcoe, Sep 03 2016

The sequence is conjectured to be infinite.

Cf. A000040, A020450.

Table[Select[Map[FromDigits, Permutations[ConstantArray[1, n + 1] ~Join~ ConstantArray[2, n], {2 n + 1}]], PrimeQ], {n, 5}] // Flatten (* Michael De Vlieger, Sep 04 2016 *)

listp(nn) = { forprime(p=2, nn, d = digits(p); if ((vecmin(d) == 1) && (vecmax(d) == 2) && (#select(x->x==1, d) == #select(x->x==2, d) +1), print1(p, ", ");););} \\ Michel Marcus, Sep 04 2016

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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A334170 Emirps containing only the digits 1 and 2.

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A276461 Prime numbers whose digits are k+1 1's and k 2's for some k >= 1.

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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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