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A061448
a(1) = 2; a(n+1) = smallest prime > a(n) with leading digit equal to final digit of a(n).
3
2, 23, 31, 101, 103, 307, 701, 1009, 9001, 10007, 70001, 100003, 300007, 700001, 1000003, 3000017, 7000003, 30000001, 100000007, 700000001, 1000000007, 7000000001, 10000000019, 90000000019, 90000000023, 300000000077
OFFSET
1,1
COMMENTS
From R. J. Mathar, Feb 15 2012: (Start)
Starting with other primes we find:
3, 31, 101, 103, 307, 701, 1009, 9001, 10007,.. or
5, 53, 307, 701, 1009, 9001, 10007, 70001, 10000.... or
7, 71, 101, 103, 307, 701, 1009, 9001, 10007, 70001 .. or
11, 13, 31, 101, 103, 307, 701, 1009, 9001,.. or
13, 31, 101, 103, 307, 701, 1009, 9001,.. or
17, 71, 101, 103, 307, 701, 1009, 9001, 10007,.. or
19, 97, 701, 1009, 9001, 10007, 70001, 100003,.. (End)
FORMULA
a(n) = A054262(n-1), n>2. - R. J. Mathar, Jan 30 2009
EXAMPLE
a(5) = 103, hence a(6) = 307.
MAPLE
A061448 := proc(n)
option remember;
local a, sdig, adgs, ad ;
if n = 1 then
2;
else
sdig := procname(n-1) mod 10 ;
a := nextprime(procname(n-1)) ;
while true do
adgs := convert(a, base, 10) ;
ad := op(-1, adgs) ;
if op(-1, adgs) = sdig then
if isprime(a) then
return a;
end if;
elif ad > sdig then
a := sdig*10^nops(adgs) ;
elif ad < sdig then
a := sdig*10^(nops(adgs)-1) ;
end if;
a := nextprime(a) ;
end do:
end if;
end proc: # R. J. Mathar, Feb 15 2013
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A049556 A049580 A373780 * A007510 A117242 A144550
KEYWORD
nonn,base
AUTHOR
Amarnath Murthy, May 03 2001
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), May 17 2001
Terms from a(18) added by Patrick De Geest, Jun 04 2001
STATUS
approved