A340634 -id:A340634 - cp's OEIS frontend

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

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

All terms have first digit 2, 3 or 4.

			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.

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

Cf. A037276, A340634, A340636.

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));

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

Original entry on oeis.org

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

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

			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.

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

Cf. A037276, A340633, A340634.

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);

cp's OEIS Frontend

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

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