A335301 a(n) = prime(n+1) mod (10^k) where k is the least positive integer such that floor(prime(n)/(10^k)) = floor(prime(n+1)/(10^k)) and prime(n) denotes the n-th prime number.

3, 5, 7, 11, 3, 7, 9, 23, 9, 31, 7, 41, 3, 7, 53, 9, 61, 7, 71, 3, 9, 83, 9, 97, 101, 3, 7, 9, 13, 27, 31, 7, 9, 49, 51, 7, 63, 7, 73, 9, 81, 91, 3, 7, 9, 211, 23, 7, 9, 33, 9, 41, 51, 7, 63, 9, 71, 7, 81, 3, 93, 307, 11, 3, 7, 31, 7, 47, 9, 53, 9, 67, 73, 9

Offset

1,1

Comments

In other words, a(n) is the smallest suffix to be overlaid on the decimal representation of the n-th prime number to obtain the next prime number.

This sequence has similarities with A274206; here we consider consecutive prime numbers, there consecutive nonnegative integers.

There are no two consecutive equal terms.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

a(n) <= prime(n+1) with equality iff prime(n+1) is the least prime number with its number of digits and leading digit.

Example

For n = 42:
- prime(42) = 181 and prime(43) = 191,
- floor(181/(10^1)) = 18 <> 19 = floor(191/(10^1)),
- floor(181/(10^2)) = 1 = floor(191/(10^2)),
- so a(42) = 191 mod (10^2) = 91.

Prog

(PARI) { base=10; p=2; forprime (q=p+1, 379, for (k=0, oo, m=base^k; if (q\m == p\m, print1 (q%m", "); p=q; break))) }

Crossrefs

Cf. A274206, A335302 (binary variant).

Sequence in context: A088635 A296550 A031255 * A235379 A174839 A245462

Adjacent sequences: A335298 A335299 A335300 * A335302 A335303 A335304

Keyword

nonn,base

Author

Rémy Sigrist, May 31 2020

Status

approved