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
Examples
1, 13, 139, 13913, 1391363, 1391363107,..., etc. are not composite.
Programs
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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}]
Comments