A094043 Alternate composite and prime numbers not included earlier such that every partial concatenation is a prime: a(2n) is prime and a(2n-1) is not prime.

1, 3, 9, 13, 63, 107, 27, 67, 39, 23, 49, 29, 99, 439, 207, 41, 357, 229, 77, 139, 69, 839, 133, 239, 121, 317, 187, 53, 33, 1291, 177, 557, 171, 1753, 323, 19, 519, 953, 231, 523, 321, 251, 327, 31, 299, 2203, 747, 101, 81, 1741, 291, 6779, 261, 1549, 1463, 97, 297

Offset

1,2

Comments

Conjecture: 2 and 5 are the only two nonmembers.

Links

Table of n, a(n) for n=1..57.

Example

1, 13, 139, 13913, 1391363, 1391363107,..., etc. are not composite.

Mathematica

p = Prime[ Range[ 1500]]; np = Drop[ Complement[ Range[ 1500], p], 1]; a[1] = 1; a[n_] := a[n] = Block[{k = 1, q = Flatten[ IntegerDigits[ # ] & /@ Table[ a[i], {i, 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. A088614, A094045.

Sequence in context: A316920 A018292 A089147 * A134190 A047905 A134904

Adjacent sequences: A094040 A094041 A094042 * A094044 A094045 A094046

Keyword

nonn,base

Author

Robert G. Wilson v, Apr 23 2004

Status

approved