A073805 -id:A073805 - cp's OEIS frontend

A083814 Duplicate of A073805.

1, 2, 4, 6, 10, 16, 18, 20, 24, 25, 26, 28, 36, 42, 50, 52, 58, 61, 62, 63, 66, 68, 70, 80, 81

Offset: 1

dead

A372197 Primes that can be represented as k*R(k) + 1, where R(k) is the reverse of k.

2, 5, 11, 17, 37, 41, 101, 251, 401, 491, 641, 811, 977, 1009, 1301, 1459, 1601, 1613, 2269, 2297, 2521, 4001, 4357, 4931, 5741, 5849, 8101, 9001, 10891, 12071, 12101, 13001, 14621, 16001, 17291, 19441, 22961, 23633, 26681, 27011, 30493, 31541, 34781, 38153, 42283, 42751, 46061, 58481, 66457

Offset: 1

Robert Israel, Jul 03 2024

Values of the primes corresponding to A073805, sorted and with duplicates removed.

Most terms can be obtained in two ways, corresponding to x * R(x) + 1 and R(x) * x + 1 or more generally (10^i * x) * R(x) + 1 and (10^i * R(x)) * x + 1, where R(x) <> x and x doesn't end in 0 so R(R(x)) = x. The first term that can be obtained in four ways is 1015561 = 1560 * 651 + 1 = 2730 * 372 + 1 = 3720 * 273 + 1 = 6510 * 156 + 1.

			a(1) = 2 = 1 * 1 + 1.
a(3) = 11 = 10 * 1 + 1.
a(13) = 977 = 16 * 61 + 1.

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

Cf. A004086, A073805.

N:= 6: # for terms <= 10^N where N is even
S:= {}:
for x from 1 to 10^(N/2)-1 do
  if x mod 10 = 0 then next fi;
  r:= rev(x);
  if r < x then next fi;
  v:= x*r;
  for i from 0 do
    w:= 10^i*v+1;
    if w > 10^N then break fi;
    if isprime(w) then S:= S union {w} fi;
  od
od:
sort(convert(S,list));

A383357 Integers m such that R(Sum_{k=1..m} (10^k+k)) is prime, where R is the digit reversal function A004086.

Original entry on oeis.org

1, 2, 4, 20, 34, 35, 77, 158, 181, 401, 973, 3517, 6818

Offset: 1

Claude H. R. Dequatre, Apr 24 2025

The primes referred to in the above definition consist, after the rightmost few digits >= 1, of only 1's and their size increases quickly with m as shown below.
  m                 Primes        Number of digits of primes
---------------------------------------------------------------
   1                      11               2
   2                     311               3
   4                    2111               4
  20                23111..1              21
.                      .                   .
.                      .                   .
 401             11719111..1             402
 973            169485111..1             974
3517           3157927111..1            3518
6818          18075343111..1            6819
.
.
If it exists a(14), >= 10^4.

			1 is a term because 10^1+1 = 11 and its digit reversal is 11, which is prime.
2 is a term because 10^1+1 + 10^2+2 = 113 and its digit reversal is 311, a prime.
3 is not a term because 10^1+1 + 10^2+2 + 10^3+3 = 1116 and R(1116) = 6111, not prime.

Cf. A000040, A004086, A073805.

for(n=1,400,my(s=fromdigits(Vecrev(digits(sum(k=1,n,10^k+k)))));if(ispseudoprime(s),print1(n", ")));

cp's OEIS Frontend

A083814 Duplicate of A073805.

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A372197 Primes that can be represented as k*R(k) + 1, where R(k) is the reverse of k.

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A383357 Integers m such that R(Sum_{k=1..m} (10^k+k)) is prime, where R is the digit reversal function A004086.

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PARI