A077202 a(1) = 1, a(n) = smallest number such that the concatenation of two successive terms gives a prime which has not occurred earlier.

1, 1, 3, 1, 7, 1, 9, 7, 3, 7, 9, 11, 3, 11, 17, 3, 13, 1, 27, 1, 37, 3, 17, 9, 19, 1, 39, 7, 19, 3, 31, 19, 7, 27, 7, 33, 7, 39, 11, 23, 3, 47, 9, 29, 3, 49, 1, 49, 9, 37, 9, 41, 9, 47, 21, 1, 51, 13, 19, 9, 53, 23, 9, 67, 3, 53, 33, 13, 21, 11, 29, 17, 21, 13, 27, 11, 51, 19, 13, 61

Offset

1,3

Comments

Conjecture: Every odd prime occurs in this sequence infinitely many times.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Maple

b:= proc() true end:
a:= proc(n) option remember; local h, k, p;
      if n=1 then 1
    else h:= a(n-1);
         for k do p:=parse(cat(h, k));
           if b(p) and isprime(p) then break fi
         od; b(p):= false; k
      fi
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 18 2015

Prog

(PARI) A077202(nmax)= { local(a, tst, hadp, hSet) ; a=[1] ; hadp=[1] ; for(n=2, nmax, for(new=1, 10000, tst=Str(eval(a[n-1]) eval(new)) ; tst=eval(tst) ; if(isprime(tst), hSet=Set(hadp) ; if( setsearch(hSet, tst)==0, hadp=concat(hadp, tst) ; a=concat(a, new) ; break ; ) ; ) ; ) ; ) ; return(a) ; } { print(A077202(80)) ; } - R. J. Mathar, May 19 2006

Crossrefs

Cf. A082238.

Sequence in context: A163117 A099749 A210442 * A086665 A273013 A050521

Adjacent sequences: A077199 A077200 A077201 * A077203 A077204 A077205

Keyword

base,nonn

Author

Amarnath Murthy, Nov 02 2002

Extensions

Corrected and extended by R. J. Mathar, May 19 2006

Offset corrected by Alois P. Heinz, Sep 18 2015

Status

approved