A070329 Nontrivial numbers in which inserting, prefixing or suffixing a 1 anywhere yields only composite numbers.

12, 16, 22, 30, 34, 36, 45, 48, 55, 58, 61, 72, 78, 84, 85, 87, 90, 96, 100, 108, 111, 112, 114, 121, 124, 126, 133, 135, 141, 142, 144, 150, 154, 156, 159, 165, 166, 168, 175, 177, 178, 184, 189, 192, 196, 198, 199, 202, 204, 205, 210, 219, 220, 226, 232, 240

Offset

1,1

Comments

This excludes numbers == 2 mod 3 (A016789).

Links

Table of n, a(n) for n=1..56.

Example

26 is a member as the three numbers 126, 216 and 261 obtained by placing a 1 at all possible places are composite.

Maple

anz := 0:for i from 1 to 1500 do b := convert(i, base, 10):s := sum(b[l], l=1..nops(b)): if((s mod 3)<>2) then ok := true:for j from 0 to nops(b) do q := sum(b[k]*10^(k-1), k=1..j):q := q+10^(j):q := q+sum(b[k]*10^k, k=j+1..nops(b)): if(isprime(q)) then ok := false:fi:od: if(ok=true) then anz := anz+1:a[anz] := i:fi:fi:od:seq(a[l], l=1..anz); # Sascha Kurz, Jan 26 2003

Crossrefs

Cf. A002808, A016789, A070328.

Sequence in context: A344079 A240052 A363798 * A064695 A162824 A335224

Adjacent sequences: A070326 A070327 A070328 * A070330 A070331 A070332

Keyword

base,nonn

Author

Amarnath Murthy, May 11 2002

Extensions

More terms from Olaf Voß, Jan 21 2003

Status

approved