A262254 a(1) = 11; for n>1, a(n) is the smallest prime that starts with the least significant digit of the previous term and has not occurred earlier.

11, 13, 31, 17, 71, 19, 97, 73, 37, 79, 907, 701, 101, 103, 307, 709, 911, 107, 719, 919, 929, 937, 727, 733, 311, 109, 941, 113, 313, 317, 739, 947, 743, 331, 127, 751, 131, 137, 757, 761, 139, 953, 337, 769, 967, 773, 347, 787, 797, 7001, 149, 971, 151, 157, 7013, 349, 977, 7019, 983

Offset: 1

Author

Maghraoui Abdelkader, Sep 16 2015

Keywords

• nonn
• base

Comments

This sequence is different from A089755, as this one does not include single-digit primes.

This sequence is different from A089755, for which a(n+1) uses all the digit of a(n) except the most-significant digit of a(n).

In this sequence, a(n+1) uses only the least-significant digit of a(n).

Examples

			a(3) = 31 where the most significant digit of 31 is 3, which is the least significant digit of a(2) = 13.
		

Links

• Maghraoui Abdelkader, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A076653, A082238, A089755, A107809, A180022.

Programs

Mathematica

f[s_List] := Block[{lsd = Mod[s[[-1]], 10], p = 3}, While[ IntegerDigits[p][[1]] != lsd || MemberQ[s, p], p = NextPrime@ p]; Append[s, p]]; s = {11}; s = Nest[f, s, 70] (* Robert G. Wilson v, Sep 16 2015 *)

PARI

msd(n)=(n\10^(#Str(n)-1)); l1=1;l3=1;l7=1;l9=1; q=1; lsd(n)=n%10;
t1 = vector(200); i=1;forprime(n=11,10000, if( digits(n)[1]==1,t1[i]=n; i=i+1 ; )) ;
t3 = vector(130); i=1;forprime(n=31,3900 ,  if( digits(n)[1]==3,t3[i]=n; i=i+1 ; ));
t7 = vector(130); i=1;forprime(n=71,70000, if( digits(n)[1]==7,t7[i]=n; i=i+1 ; )) ;
t9 = vector(130); i=1;forprime(n=97,90000, if( digits(n)[1]==9,t9[i]=n; i=i+1 ; )) ;lsd(n)=n%10;
t = vector(200);
findnextnumber(m) =
{if(lsd(m)==1, l1=t1[i1] ; i1=i1+1;return(l1);); if(lsd(m)==3, l3=t3[i3];  i3=i3+1 ; return(l3););
if(lsd(m)==7, l7=t7[i7] ; i7=i7+1;return(l7);); if(lsd(m)==9, l9=t9[i9];  i9=i9+1;return(l9);); }
i1=1;  i3=1;  i7=1;  i9=1;  j=1;s=11;   for(n=1,200,   p=findnextnumber(s) ; t[j]=p; s=p;j++);for(i=1,200, print1(t[i],", ") )