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 *)
A055011
a(n+1) = next smallest prime beginning with a(n) when written in binary, starting with 2.
Original entry on oeis.org
2, 5, 11, 23, 47, 191, 383, 3067, 12269, 196307, 6281839, 50254717, 201018869, 804075479, 1608150959, 102921661397, 1646746582367, 13173972658937, 105391781271503, 210783562543007, 3372537000688127, 26980296005505019, 863369472176160611, 6906955777409284889
Offset: 0
-
a055011 n = a055011_list !! n
a055011_list = iterate a208241 2 -- Reinhard Zumkeller, Feb 14 2013
-
A055011 := proc(n)
option remember;
if n = 0 then
2 ;
else
A208241(procname(n-1)) ;
end if;
end proc: # R. J. Mathar, May 06 2017
A261200
Minimal prime concatenation sequence with base 2 and seed 1.
Original entry on oeis.org
1, 10, 101, 1011, 10111, 101111, 10111111, 101111111, 101111111011, 10111111101101, 101111111011010011, 10111111101101001101111, 10111111101101001101111101, 1011111110110100110111110101, 101111111011010011011111010111, 1011111110110100110111110101111
Offset: 1
In base 2, the least prime starting with seed 1 is 10; the least prime starting with 10 is 101; the least prime starting with 101 is 1011. Triangular format:
1
10
101
1011
10111
101111
10111111
101111111
101111111011
-
b = 2; s = {{1}};
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], {30}]; Map[FromDigits, s]
Map[FromDigits, s] (* A261200 *)
Map[FromDigits[#, b] &, s] (* A261201 *)
(* Peter J. C. Moses, Aug 06 2015 *)
Original entry on oeis.org
3, 7, 29, 59, 239, 479, 3833, 30671, 61343, 981493, 3925973, 62815573, 502524587, 2010098351, 16080786809, 1029170355779, 4116681423119, 65866902769909, 263467611079637, 2107740888637103, 134895416872774619, 17266613359715151259, 1105063255021769680613
Offset: 1
-
b = 2; s = {{1}}; 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], {30}]; Map[FromDigits, s]; Map[FromDigits, s] (* A261200 *)
Map[FromDigits[#, b] &, s] (* A261201 *)
(* Peter J. C. Moses, Aug 06 2015 *)
Showing 1-4 of 4 results.
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