A048549
a(n+1) is next smallest prime beginning with a(n), initial prime is 2.
Original entry on oeis.org
2, 23, 233, 2333, 23333, 2333321, 233332117, 2333321173, 233332117313, 23333211731399, 2333321173139903, 2333321173139903173, 23333211731399031733, 2333321173139903173301, 2333321173139903173301021
Offset: 1
Similar to but different from
A069603.
-
b = 10; s = {{2}};
Do[NestWhile[# + 1 &, 0, ! (PrimeQ[FromDigits[tmp = Join[Last[s], (nn = #;
IntegerDigits[nn - Sum[b^n, {n, l = NestWhile[# + 1 &, 1, ! (nn - (Sum[b^n, {n, #}]) < 0) &] - 1}], b, l + 1])], b]]) &]; AppendTo[s, tmp], {20}]; Map[FromDigits, s] (* Peter J. C. Moses, Aug 06 2015 *)
A048553
a(n+1) is next smallest prime beginning with a(n), initial prime is 11.
Original entry on oeis.org
11, 113, 11311, 113111, 1131113, 11311133, 1131113353, 113111335313, 11311133531339, 113111335313399, 1131113353133993, 113111335313399321, 11311133531339932153, 1131113353133993215379, 113111335313399321537911
Offset: 0
-
f:= proc(n)
local p, d;
for d from 1 do
p:= nextprime(n*10^d);
if p < (n+1)*10^d then return p fi
od
end proc:
A[1]:= 11:
for n from 2 to 20 do A[n]:= f(A[n-1]) od:
seq(A[n], n=1..20); # Robert Israel, Aug 16 2015
-
a = {11}; Do[k = 1; w = IntegerDigits[a[[n - 1]]];
While[CompositeQ@ FromDigits[Join[w, IntegerDigits@ k]], k += 2];
AppendTo[a, FromDigits[Join[w, IntegerDigits@ k]]], {n, 2, 15}]; a (* Michael De Vlieger, Sep 21 2015 *)
A048552
a(n+1) is next smallest prime beginning with a(n), initial prime is a(0) = 7.
Original entry on oeis.org
7, 71, 719, 7193, 71933, 719333, 71933317, 719333177, 71933317711, 7193331771103, 71933317711039, 7193331771103939, 719333177110393913, 7193331771103939133, 719333177110393913323, 71933317711039391332309, 719333177110393913323097, 719333177110393913323097047
Offset: 0
-
f:= proc(n) option remember; local q,d,v;
q:=procname(n-1);
for d from 1 do
v:= nextprime(q*10^d);
if v < (q+1)*10^d then return v fi
od
end proc:
f(0):= 7:
map(f, [$0..20]); # Robert Israel, Jan 26 2020
-
Nest[Function[{a, n}, Append[#, Catch@ Do[Do[If[PrimeQ@ #, Throw@ #; Break[], #] &@ FromDigits[n~Join~PadLeft[IntegerDigits[(5 j - 4 + Mod[3 j + 2, 4])/2], i]], {j, 4*10^(i - 1)}], {i, Infinity}]]] @@ {#, IntegerDigits[#[[-1]] ]} &, {7}, 17] (* Michael De Vlieger, Jan 26 2020 *)
-
next_A048552(p)=for(i=1,oo,my(q=nextprime(p*=10));q-p>10^i||return(q))
A048552(n,p=7)=vector(n,i,i>1&&p=next_A048552(p);p) \\ M. F. Hasler, Jan 26 2020
A048550
a(n+1) is the next smallest prime beginning with a(n), initial prime is 3.
Original entry on oeis.org
3, 31, 311, 3119, 31193, 3119309, 31193093, 311930933, 31193093317, 311930933179, 3119309331797, 311930933179703, 31193093317970371, 3119309331797037107, 311930933179703710759, 31193093317970371075907
Offset: 0
-
f:= proc(n) local d,a;
for d from 1 do
for a from 10^d*n+1 by 2 to 10^d*(n+1) do
if isprime(a) then return a fi
od od
end proc:
R:= 3: x:= 3:
for i from 2 to 30 do
x:= f(x);
R:= R, x;
od:
R; # Robert Israel, Dec 13 2023
A048555
p(n+1) is next smallest prime beginning with p(n), initial prime is 17.
Original entry on oeis.org
17, 173, 1733, 17333, 1733309, 173330917, 1733309173, 17333091733, 1733309173319, 173330917331917, 17333091733191701, 1733309173319170103, 173330917331917010357, 17333091733191701035703
Offset: 0
A048551
p(n+1) is next smallest prime beginning with p(n), initial prime is 5.
Original entry on oeis.org
5, 53, 5303, 530303, 53030317, 530303173, 53030317313, 530303173133, 53030317313327, 53030317313327047, 5303031731332704703, 530303173133270470327, 5303031731332704703273, 530303173133270470327321
Offset: 0
A048554
p(n+1) is next smallest prime beginning with p(n), initial prime is 13.
Original entry on oeis.org
13, 131, 1319, 131909, 13190909, 1319090933, 131909093341, 13190909334101, 1319090933410141, 131909093341014131, 13190909334101413129, 131909093341014131297, 13190909334101413129739
Offset: 0
Showing 1-7 of 7 results.