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

1,1

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).

Links

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

Example

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

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 *)

Prog

(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], ", ") )

Crossrefs

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

Sequence in context: A056251 A222805 A089755 * A082238 A179551 A054262

Adjacent sequences: A262251 A262252 A262253 * A262255 A262256 A262257

Keyword

nonn,base

Author

Maghraoui Abdelkader, Sep 16 2015

Status

approved