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

Author

Claude H. R. Dequatre, Apr 24 2025

Keywords

• nonn
• base
• more

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.

Examples

			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.
		

Crossrefs

Cf. A000040, A004086, A073805.

Programs

PARI

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