A340633 -id:A340633 - cp's OEIS frontend

A340634 Numbers k such that k + A037276(k) is prime.

1, 6, 14, 18, 22, 26, 34, 36, 38, 46, 48, 62, 66, 74, 106, 108, 110, 122, 134, 146, 156, 166, 170, 174, 178, 194, 196, 198, 206, 226, 230, 254, 262, 274, 278, 290, 294, 298, 306, 318, 354, 362, 374, 386, 392, 394, 416, 420, 422, 426, 458, 466, 468, 490, 502, 504, 516, 526, 528, 530, 532, 544, 562

Offset: 1

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

All terms except 1 are even.

			a(3) = 14 is a term because 14 + A037276(14) = 14 + 27 = 41 is prime.

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

Cf. A037276, A340633, A340636.

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:
select(t -> isprime(t + A037276(t)), [1,seq(i,i=3..1000)]);

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

A340634 Numbers k such that k + A037276(k) is prime.

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