

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.


5



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
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OFFSET

1,2


COMMENTS

Conjecture: all odd numbers not of the type 10k+5 are members.
Some of the larger entries may only correspond to probable primes.
Values corresponding to a(6)=27 (A083755(5)) through a(59)=363 (A083755(58), a 149digit value) have been certified prime with Primo.  Rick L. Shepherd, May 10 2003
Since we begin with 1 and thereafter have more than a single decimal digit, all terms must be in A045572, the sequence that contains all positive integers relatively prime to 10.  Michael De Vlieger, Oct 30 2020.


LINKS



EXAMPLE

13,137,13711, etc. are primes.(1379 is not a prime) hence 11 is the next member after 7.


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 *)


PROG

(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}


CROSSREFS



KEYWORD

base,nonn


AUTHOR

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 06 2003


EXTENSIONS



STATUS

approved



