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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 7 05:00 EDT 2022. Contains 357270 sequences. (Running on oeis4.)