A083754 a(1) = 1 and then smallest odd number not occurring earlier such that the concatenation a(1)a(2)a(3)... is a prime.
1, 3, 7, 11, 9, 27, 63, 31, 53, 21, 13, 83, 33, 39, 49, 51, 77, 87, 307, 29, 229, 281, 151, 173, 481, 41, 99, 157, 177, 17, 357, 213, 231, 171, 271, 557, 67, 113, 463, 159, 119, 57, 247, 147, 563, 409, 353, 391, 179, 1051, 209, 19, 153, 621, 287, 567, 313, 117, 363
Offset: 1
Examples
13,137,13711, etc. are primes.(1379 is not a prime) hence 11 is the next member after 7.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..501
- Michael De Vlieger, Plot of a(n) for 1 <= n <= 500, showing congruency of a(n) with 1 (orange), 3 (green), 7 (blue), or 9 (magenta) (mod 10).
Programs
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Mathematica
Block[{c = 1, a = {1}, f, g}, f[m_, n_] := m*10^(1 + Floor[Log10[n]]) + n; g[n_] := (5 n + Mod[3 n + 2, 4] - 4)/2; Do[Block[{j = 2, k, d, t}, While[Nand[FreeQ[a, Set[k, g[j] ]], PrimeQ[Set[d, f[c, k]]]], j++]; c = d; AppendTo[a, k]], {i, 59}]; a] (* Michael De Vlieger, Oct 30 2020 *) -
PARI
{used_before(v, n) = for (l=1,matsize(v)[2], if(v[l]==n, return(1))); return(0)} {A083754=[1]; p=A083754[1]; A083755=[]; print1(A083754[1],","); for (m=2,151, k=1; while (used_before(A083754,k)||!isprime(tmp_p=p*(10^length(Str(k)))+k), k=k+2); p=tmp_p; A083755=concat(A083755,p); A083754=concat(A083754,k); print1(A083754[m],",")); A083755}
Extensions
More terms from Rick L. Shepherd, May 08 2003
Comments