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

Author

Amarnath Murthy, Nov 02 2002

Keywords

• base
• nonn

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

Crossrefs

Cf. A082238.

Programs

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

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

Extensions

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

Offset corrected by Alois P. Heinz, Sep 18 2015