

A228323


a(1)=1; thereafter a(n) is the smallest number m not yet in the sequence such that at least one of the concatenations a(n1)m or ma(n1) is prime.


6



1, 3, 2, 9, 5, 21, 4, 7, 6, 13, 10, 19, 16, 27, 8, 11, 15, 23, 12, 17, 20, 29, 14, 33, 26, 47, 18, 31, 25, 39, 22, 37, 24, 41, 30, 49, 34, 57, 28, 43, 36, 59, 32, 51, 38, 53, 42, 61, 45, 67, 58, 69, 55, 63, 44, 81, 35, 71, 48, 77, 50, 87, 62, 99, 40, 73, 46
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OFFSET

1,2


COMMENTS

Does every number appear in the sequence?
If a(n) is coprime to 10, then a(n+1) exists by Dirichlet's theorem.  Eric M. Schmidt, Aug 20 2013 [In more detail: let a(n) have d digits, and consider the arithmetic progression k*10^d + a(n), and apply Dirichlet's theorem. This gives a number k such that the concatenation ka(n) is prime. N. J. A. Sloane, Nov 08 2020]
The argument in A068695 shows that a(n) always exists.  N. J. A. Sloane, Nov 11 2020


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Eric Angelini, Primes by concatenation, Posting to the Sequence Fans Mailing List, Aug 14 2013.
Index entries for primes involving decimal expansion of n


MATHEMATICA

f[s_] := Block[{k = 2, idj = IntegerDigits@ s[[1]]}, While[idk = IntegerDigits@ k; MemberQ[s, k]  ( !PrimeQ@ FromDigits@ Join[idj, idk] && !PrimeQ@ FromDigits@ Join[idk, idj]), k++]; Append[s, k]]; Nest[f, {1}, 66] (* Robert G. Wilson v, Aug 20 2013 *)


CROSSREFS

See A228324 for the primes that arise.
Cf. A069695, A228325.
Sequence in context: A033313 A231442 A319107 * A140590 A329211 A164279
Adjacent sequences: A228320 A228321 A228322 * A228324 A228325 A228326


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane, Aug 20 2013


EXTENSIONS

More terms from Alois P. Heinz, Aug 20 2013


STATUS

approved



