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 A215419 Primes that remain prime when a single digit 3 is inserted between any two consecutive digits or as the leading or trailing digit. 25
 7, 11, 17, 31, 37, 73, 271, 331, 359, 373, 673, 733, 1033, 2297, 3119, 3461, 3923, 5323, 5381, 5419, 6073, 6353, 9103, 9887, 18289, 23549, 25349, 31333, 32933, 33349, 35747, 37339, 37361, 37489, 47533, 84299, 92333, 93241, 95093, 98491, 133733, 136333, 139333 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Robert Israel, Table of n, a(n) for n = 1..150 EXAMPLE 18289 is prime and also 182893, 182839, 182389, 183289, 138289, 318289. MAPLE A215419:=proc(q, x) local a, b, c, d, i, n, ok; for n from 1 to q do a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=ithprime(n); ok:=1; for i from 0 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(ithprime(n)); fi; od; end: A215419(1000, 3); # Alternative: filter:= proc(n) local L, d, k, M; if not isprime(n) then return false fi; L:= convert(n, base, 10); d:= nops(L); for k from 0 to d do M:= [seq(L[i], i=1..k), 3, seq(L[i], i=k+1..d)]; if not isprime(add(M[i]*10^(i-1), i=1..d+1)) then return false fi; od; true end proc; select(filter, [seq(i, i=3..2*10^5, 2)]); # Robert Israel, Oct 09 2017 MATHEMATICA ins@n_:=Insert[IntegerDigits@n, 3, #]&/@Range@(IntegerLength@n+1); Cases[{#, FromDigits@#&/@ins@#}&/@ Cases[Range[11, 70000], _?PrimeQ], {_, {_?PrimeQ..}}][[All, 1]] (* Hans Rudolf Widmer, Dec 21 2023 *) CROSSREFS Cf. A215417, A069246, A215420, A215421 Sequence in context: A068674 A156112 A158594 * A107642 A079651 A178386 Adjacent sequences: A215416 A215417 A215418 * A215420 A215421 A215422 KEYWORD nonn,base AUTHOR Paolo P. Lava, Aug 10 2012 STATUS approved

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Last modified July 14 05:06 EDT 2024. Contains 374291 sequences. (Running on oeis4.)