A094045 Alternate composite and prime numbers not included earlier such that every concatenation of a pair of terms is a prime: a(2n) is prime and a(2n-1) is nonprime.

1, 3, 49, 19, 9, 7, 27, 11, 51, 13, 21, 29, 39, 17, 33, 23, 57, 37, 69, 47, 87, 31, 63, 43, 91, 61, 99, 41, 77, 53, 81, 67, 93, 71, 119, 59, 123, 73, 121, 97, 117, 79, 111, 103, 141, 101, 159, 113, 143, 89, 153, 83, 177, 109, 133, 157, 189, 127, 207, 139, 169, 151, 171, 131

Offset

1,2

Comments

Conjecture: 2 and 5 are the only two nonmembers.

Links

Table of n, a(n) for n=1..64.

Example

a(3)=49 => 349 is a prime but not necessarily 1349, which by the way it
is not.

Mathematica

p = Prime[ Range[ 500]]; np = Drop[ Complement[ Range[ 500], p], 1]; a[1] = 1; a[n_] := a[n] = Block[{k = 1, q = IntegerDigits[a[n - 1]]}, If[ EvenQ[n], While[ !PrimeQ[ FromDigits[ Join[q, IntegerDigits[ p[[k]] ]]]], k++ ]; q = p[[k]]; p = Delete[p, k]; q, While[ !PrimeQ[ FromDigits[ Join[q, IntegerDigits[ np[[k]] ]]]], k++ ]; q = np[[k]]; np = Delete[np, k]; q]]; Table[ a[n], {n, 60}]

Crossrefs

Cf. A094043, A094044.

Sequence in context: A033493 A334421 A359261 * A033494 A188380 A252171

Adjacent sequences: A094042 A094043 A094044 * A094046 A094047 A094048

Keyword

nonn,base

Author

Robert G. Wilson v, Apr 23 2004

Status

approved