A068690 Primes such that all digits (except perhaps the least significant digit) are even.
2, 3, 5, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89, 223, 227, 229, 241, 263, 269, 281, 283, 401, 409, 421, 443, 449, 461, 463, 467, 487, 601, 607, 641, 643, 647, 661, 683, 809, 821, 823, 827, 829, 863, 881, 883, 887, 2003, 2027, 2029, 2063, 2069, 2081, 2083, 2087
Offset: 1
Examples
2 is in the sequence even though the least significant digit of 2 is even instead of odd. - _David A. Corneth_, Sep 18 2019
Links
- Zak Seidov, Table of n, a(n) for n = 1..10775 (all terms < 10^8.)
Programs
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Haskell
a068690 n = a068690_list !! (n-1) a068690_list = filter (all (`elem` "02468") . init . show) a000040_list -- Reinhard Zumkeller, Apr 28 2014
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Mathematica
(*returns true if all but the last digit of n is even, false o.w.*) f[n_] := Module[{a, l, i, r = True}, a = IntegerDigits[n]; l = Length[a]; For[i = 1, i < l, i++, If[Mod[a[[i]], 2] == 1, r = False; Break[ ]]]; r]; Select[Range[1, 4*10^3], PrimeQ[ # ] && f[ # ] &] m = 7; Prepend[Reap[Do[If[PrimeQ[fd = FromDigits[{a[1], a[2], a[3], a[4], a[5], a[6], a[m]}]], Sow[fd]], {a[1], 0, 8, 2}, {a[2], 0, 8, 2}, {a[3], 0, 8, 2}, {a[4], 0, 8, 2}, {a[5], 0, 8, 2}, {a[6], 0, 8, 2}, {a[m], 1, 9, 2}]][[2, 1]], 2] (* all terms < 10^8. Zak Seidov, Jan 29 2013 *) Select[ Prime@ Range[10000], ContainsAll[{0, 2, 4, 6, 8}, Most@ IntegerDigits[#]] &] (* From version 10. Mikk Heidemaa, Feb 08 2016 *) Select[Prime[Range[400]],AllTrue[Most[IntegerDigits[#]],EvenQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 18 2019 *)
Extensions
Definition rephrased by N. J. A. Sloane, Dec 11 2007
Comments