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

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

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..13.

Example

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.

Prog

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

Crossrefs

Cf. A000040, A004086, A073805.

Sequence in context: A069535 A108866 A259122 * A059206 A294230 A332626

Adjacent sequences: A383354 A383355 A383356 * A383358 A383359 A383360

Keyword

nonn,base,more

Author

Claude H. R. Dequatre, Apr 24 2025

Status

approved