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%I #16 Nov 21 2024 21:25:38
%S 2,3,5,7,11,23,17,29,13,47,19,37,41,53,61,43,59,31,67,83,71,89,73,101,
%T 79,103,97,113,227,109,223,107,229,131,257,139,277,149,233,151,239,
%U 157,263,179,283,167,293,181,269,137,409,127,349
%N a(n+1) is the smallest prime not already in the sequence which shares no digit with a(n).
%C The sequence is not a permutation of prime numbers.
%C 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.
%C The first nine terms {2, 3, 5, 7, 11, 23, 17, 29, 13} coincide with A068863(1..9).
%C 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).
%C 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}.
%H Giovanni Resta, <a href="/A284146/b284146.txt">Table of n, a(n) for n = 1..10000</a>
%H Zak Seidov, <a href="/A284146/a284146.png">Graph of first 2000 terms.</a>
%t 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 *)
%Y Cf. A000040, A068863, A067581, A107801.
%K nonn
%O 1,1
%A _Zak Seidov_, Mar 20 2017