A340636 Primes of the form k + A037276(k) in more than one way.

251, 2671, 2687, 2753, 23327, 23561, 27827, 28499, 28789, 28817, 29411, 34757, 223441, 226001, 227537, 230849, 231359, 232217, 232259, 232367, 232643, 232919, 233591, 234791, 236129, 236609, 236867, 237857, 238141, 239023, 239873, 240899, 241169, 241343, 241687, 241691, 242447, 242747, 245299

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 14 2021

Keywords

• nonn
• base

Examples

			a(3) = 2687 = 170 + A037276(170) = 170 + 2517
            = 458 + A037276(458) = 458 + 2229.
The first term that occurs in more than two ways is
a(163) = 2255299 =  4180 + A037276(4180)  =  4180 + 2251119
                 = 21156 + A037276(21156) = 21156 + 2234143
                 = 29560 + A037276(29560) = 29560 + 2225739.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..7500

Crossrefs

Cf. A037276, A340633, A340634.

Programs

Maple

N:= 5*10^5: # 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:
S:= {R}:
select(s -> numboccur(s,[R])>1, S);