A070328 Numbers in which inserting, prefixing or suffixing a 1 anywhere yields only composite numbers.

2, 5, 8, 11, 12, 14, 16, 17, 20, 22, 23, 26, 29, 30, 32, 34, 35, 36, 38, 41, 44, 45, 47, 48, 50, 53, 55, 56, 58, 59, 61, 62, 65, 68, 71, 72, 74, 77, 78, 80, 83, 84, 85, 86, 87, 89, 90, 92, 95, 96, 98, 100, 101, 104, 107, 108, 110, 111, 112, 113, 114, 116, 119, 121, 122

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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 2 to 1500 do b := convert(i, base, 10):s := sum(b[l], l=1..nops(b)): 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:od:seq(a[l], l=1..anz);

Mathematica

Select[Range[200], AllTrue[FromDigits/@Table[Insert[IntegerDigits[#], 1, n], {n, IntegerLength[ #]+ 1}], CompositeQ]&] (* Harvey P. Dale, Nov 14 2023 *)

Crossrefs

Cf. A002808, A070329.

Sequence in context: A143263 A327138 A102624 * A124934 A125217 A277574

Adjacent sequences: A070325 A070326 A070327 * A070329 A070330 A070331

Keyword

base,nonn

Author

Amarnath Murthy, May 11 2002

Extensions

Corrected and extended by Sascha Kurz, Jan 26 2003

Status

approved