A332261 Numbers that yield a prime whenever a '4' is inserted between any two digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 21, 37, 39, 43, 49, 51, 57, 61, 63, 67, 73, 91, 97, 109, 129, 147, 153, 159, 171, 187, 199, 211, 223, 237, 241, 247, 259, 267, 333, 349, 357, 363, 409, 421, 423, 441, 447, 457, 463, 493, 517, 537, 541, 543, 549, 571, 579, 583, 627, 649, 681

Offset: 1

Author

Eric Fox, Feb 08 2020

Keywords

• nonn
• base

Comments

For single-digit terms, the condition is voidly satisfied: nothing can be inserted.

Examples

			10281 is in this sequence because 1(4)0281, 10(4)281, 102(4)81, and 1028(4)1 are all prime.
		

Crossrefs

Cf. A164329, A304246, A304247, A304248, A050714.

Programs

Magma

a:=[]; for k in [1..700] do s:=0; v:=Reverse(Intseq(k)); for i in [1..#v-1] do vv:=v[1..i] cat [4] cat v[i+1..#v]; p:=Seqint(Reverse(vv)); if not IsPrime(p) then break; else s:=s+1; end if; end for;  if s eq #v-1 then Append(~a,k); end if; end for; [0] cat a; // Marius A. Burtea, Feb 09 2020