

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 nth 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
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OFFSET

1,1


COMMENTS

In other words, a(n) is the smallest suffix to be overlaid on the decimal representation of the nth 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



