A088614 Alternate prime and composite numbers not included earlier such that every partial concatenation is a prime: a(2n) is composite and a(2n-1) is prime.

2, 9, 3, 27, 11, 51, 13, 33, 41, 93, 31, 99, 29, 63, 1117, 441, 503, 303, 163, 171, 59, 357, 67, 219, 113, 417, 691, 729, 239, 511, 227, 393, 211, 189, 3797, 291, 1789, 549, 419, 501, 103, 81, 3257, 39, 727, 531, 617, 69, 6883, 387, 521, 153, 1237, 287, 3391, 927

Offset

1,1

Comments

Conjecture: 1 and 5 are the only two odd nonmembers.

Links

Table of n, a(n) for n=1..56.

Example

2,29,293,29327,...etc. are primes.

Mathematica

p = Prime[ Range[ 1000]]; np = Complement[ Range[ 1000], p]; a[n_] := a[n] = Block[{k = 1, q = Flatten[ IntegerDigits[ # ] & /@ Table[ a[i], {i, n - 1}]]}, If[ OddQ[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, 56}] (* Robert G. Wilson v, Apr 23 2004 *)

Crossrefs

Cf. A088615.

Sequence in context: A171534 A163907 A237860 * A162615 A275716 A295197

Adjacent sequences: A088611 A088612 A088613 * A088615 A088616 A088617

Keyword

base,nonn

Author

Amarnath Murthy, Oct 16 2003

Extensions

More terms from Ray Chandler, Oct 18 2003

Status

approved