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 A216167 Composite numbers which yield a prime whenever a 5 is inserted anywhere in them, excluding at the end. 3
 9, 21, 57, 63, 69, 77, 87, 93, 153, 231, 381, 407, 413, 417, 501, 531, 581, 651, 669, 741, 749, 783, 791, 987, 1241, 1551, 1797, 1971, 2189, 2981, 3381, 3419, 3591, 3951, 4083, 4503, 4833, 4949, 4959, 5049, 5117, 5201, 5229, 5243, 5529, 5547, 5603, 5691, 5697 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Michael S. Branicky, Table of n, a(n) for n = 1..1923 (terms 1..300 from Paolo P. Lava) EXAMPLE 4083 is not prime but 40853, 40583, 45083 and 54083 are all primes. MAPLE with(numtheory); A216167:=proc(q, x) local a, b, c, i, n, ok; for n from 1 to q do if not isprime(n) then a:=n; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=n; ok:=1; for i from 1 to b do c:=a+9*10^i*trunc(a/10^i)+10^i*x; if not isprime(c) then ok:=0; break; fi; od; if ok=1 then print(n); fi; fi; od; end: A216167(1000, 5); MATHEMATICA Select[Range[6000], CompositeQ[#]&&AllTrue[FromDigits/@Table[Insert[IntegerDigits[#], 5, p], {p, IntegerLength[#]}], PrimeQ]&] (* Harvey P. Dale, Oct 02 2022 *) PROG (Magma) [n: n in [1..6000] | not IsPrime(n) and forall{m: t in [1..#Intseq(n)] | IsPrime(m) where m is (Floor(n/10^t)*10+5)*10^t+n mod 10^t}]; // Bruno Berselli, Sep 03 2012 (Python) from sympy import isprime def ok(n): if n < 2 or n%10 not in {1, 3, 7, 9} or isprime(n): return False s = str(n) return all(isprime(int(s[:i] + '5' + s[i:])) for i in range(len(s))) print(list(filter(ok, range(5698)))) # Michael S. Branicky, Sep 21 2021 CROSSREFS Cf. A068673, A068674, A068677, A068679, A069246, A215417, A215419-A215421, A216165, A216166, A216168, A216169. Subsequence of A053795. Sequence in context: A134717 A216980 A147169 * A246327 A320896 A127989 Adjacent sequences: A216164 A216165 A216166 * A216168 A216169 A216170 KEYWORD nonn,look,base AUTHOR Paolo P. Lava, Sep 03 2012 STATUS approved

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Last modified April 22 18:11 EDT 2024. Contains 371906 sequences. (Running on oeis4.)