A340633 Primes of the form k + A037276(k).

2, 29, 41, 233, 239, 251, 257, 269, 293, 311, 359, 383, 401, 419, 449, 467, 491, 2269, 2309, 2339, 2377, 2381, 2393, 2411, 2417, 2447, 2473, 2503, 2543, 2579, 2591, 2621, 2633, 2671, 2687, 2699, 2713, 2753, 2789, 2797, 2819, 2843, 2879, 2939, 3011, 3041, 3067, 3083, 3119, 3137, 3167, 3191, 3203

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 13 2021

Keywords

• nonn
• look
• base

Comments

All terms have first digit 2, 3 or 4.

Examples

			a(1) =   2 =  1 + A037276(1)  =  1 +   1;
a(2) =  29 =  6 + A037276(6)  =  6 +  23;
a(3) =  41 = 14 + A037276(14) = 14 +  27;
a(4) = 233 = 22 + A037276(22) = 22 + 211;
a(5) = 251 = 18 + A037276(18) = 18 + 233
           = 34 + A037276(34) = 34 + 217.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037276, A340634, A340636.

Programs

Maple

N:= 5000: # for terms <= N
dcat:= proc(L) local i, x;
  x:= L[-1];
  for i from nops(L)-1 to 1 by -1 do
    x:= 10^(1+ilog10(x))*L[i]+x
  od;
  x
end proc:
A037276:= proc(n) local F;
  F:= sort(ifactors(n)[2], (a, b) -> a[1] < b[1]);
  dcat(map(t -> t[1]$t[2], F));
end proc:
A037276(1):= 1:
R:= NULL:
for n from 1 to N/2 do
  v:= n + A037276(n);
  if v < N and isprime(v) then R:= R, v fi;
od:
sort(convert({R},list));