A284146 a(n+1) is the smallest prime not already in the sequence which shares no digit with a(n).

2, 3, 5, 7, 11, 23, 17, 29, 13, 47, 19, 37, 41, 53, 61, 43, 59, 31, 67, 83, 71, 89, 73, 101, 79, 103, 97, 113, 227, 109, 223, 107, 229, 131, 257, 139, 277, 149, 233, 151, 239, 157, 263, 179, 283, 167, 293, 181, 269, 137, 409, 127, 349

Offset

1,1

Comments

The sequence is not a permutation of prime numbers.

E.g., after calculating 2001 terms of the sequence, the first absent primes are 1973,3719,3917,7193,9137,9173,9371. It's evident that these numbers will never appear in the sequence because any last term of the sequence should use at least one of digits 1,3,7,9.

The first nine terms {2, 3, 5, 7, 11,23, 17, 29,13] coincide with A068863(1..9).

The only fixed points are a(n) for n={1, 2, 3, 4, 5, 7, 12, 13, 17, 19} are {2, 3, 5, 7, 11, 17, 37, 41, 59, 67} that is for these n's a(n)=prime(n)=A000040(n).

a (100*k) for k = 1,20: {443, 1193, 1741, 1621, 4567, 6047, 5851, 6491, 7151, 7559, 9349, 10601, 11119, 11699, 13001, 11839, 14107, 16111, 15073, 16487}.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Zak Seidov, Graph of first 2000 terms.

Mathematica

a = {2}; While[ Length[a] < 100, d = IntegerDigits@ Last@ a; p = 2; While[ Intersection[ IntegerDigits@p, d] != {} || MemberQ[a, p], p = NextPrime@ p]; AppendTo[a, p]]; a (* Giovanni Resta, Mar 21 2017 *)

Crossrefs

Cf. A000040, A068863, A067581, A107801.

Sequence in context: A048278 A247797 A068863 * A317479 A087521 A078403

Adjacent sequences: A284143 A284144 A284145 * A284147 A284148 A284149

Keyword

nonn

Author

Zak Seidov, Mar 20 2017

Status

approved