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 A070329 Nontrivial numbers in which inserting, prefixing or suffixing a 1 anywhere yields only composite numbers. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This excludes numbers numbers with sum of the digits == 2 mod 3. LINKS 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. A070328. Sequence in context: A225071 A210577 A183052 * A064695 A162824 A189763 Adjacent sequences:  A070326 A070327 A070328 * A070330 A070331 A070332 KEYWORD base,nonn AUTHOR Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 11 2002 EXTENSIONS More terms from Olaf Voss (richyfourtythree(AT)yahoo.com), Jan 21 2003 STATUS approved

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