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

1,3

Comments

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

Links

Table of n, a(n) for n=1..62.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A087121 A087052 A077557 * A075517 A248013 A088473

Adjacent sequences: A332258 A332259 A332260 * A332262 A332263 A332264

Keyword

nonn,base

Author

Eric Fox, Feb 08 2020

Status

approved