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