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a(1) = 2; a(n+1) = smallest prime > a(n) with leading digit equal to final digit of a(n).
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%I #24 Oct 26 2019 18:00:37

%S 2,23,31,101,103,307,701,1009,9001,10007,70001,100003,300007,700001,

%T 1000003,3000017,7000003,30000001,100000007,700000001,1000000007,

%U 7000000001,10000000019,90000000019,90000000023,300000000077

%N a(1) = 2; a(n+1) = smallest prime > a(n) with leading digit equal to final digit of a(n).

%C From _R. J. Mathar_, Feb 15 2012: (Start)

%C Starting with other primes we find:

%C 3, 31, 101, 103, 307, 701, 1009, 9001, 10007,.. or

%C 5, 53, 307, 701, 1009, 9001, 10007, 70001, 10000.... or

%C 7, 71, 101, 103, 307, 701, 1009, 9001, 10007, 70001 .. or

%C 11, 13, 31, 101, 103, 307, 701, 1009, 9001,.. or

%C 13, 31, 101, 103, 307, 701, 1009, 9001,.. or

%C 17, 71, 101, 103, 307, 701, 1009, 9001, 10007,.. or

%C 19, 97, 701, 1009, 9001, 10007, 70001, 100003,.. (End)

%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>

%F a(n) = A054262(n-1), n>2. - _R. J. Mathar_, Jan 30 2009

%e a(5) = 103, hence a(6) = 307.

%p A061448 := proc(n)

%p option remember;

%p local a,sdig,adgs,ad ;

%p if n = 1 then

%p 2;

%p else

%p sdig := procname(n-1) mod 10 ;

%p a := nextprime(procname(n-1)) ;

%p while true do

%p adgs := convert(a,base,10) ;

%p ad := op(-1,adgs) ;

%p if op(-1,adgs) = sdig then

%p if isprime(a) then

%p return a;

%p end if;

%p elif ad > sdig then

%p a := sdig*10^nops(adgs) ;

%p elif ad < sdig then

%p a := sdig*10^(nops(adgs)-1) ;

%p end if;

%p a := nextprime(a) ;

%p end do:

%p end if;

%p end proc: # _R. J. Mathar_, Feb 15 2013

%t a[1]=2; a[n_] := (v=IntegerDigits[a[n-1]]; v1=If[v[[ -1]]>v[[1]], v[[ -1]]*10^(Length[v]-1), If[v[[ -1]]<v[[1]]||Length[v]==1, v[[ -1]]*10^Length[v], a[n-1]]]; For[m=v1+1, !PrimeQ[m], m++ ]; m); Table[a[n], {n, 35}] (* _Farideh Firoozbakht_, Aug 30 2003 *)

%K nonn,base

%O 1,1

%A _Amarnath Murthy_, May 03 2001

%E More terms from Larry Reeves (larryr(AT)acm.org), May 17 2001

%E Terms from a(18) added by _Patrick De Geest_, Jun 04 2001