cp's OEIS Frontend

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.

%I A335301 #12 Jun 02 2020 14:09:54
%S A335301 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,
%T A335301 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,
%U A335301 63,9,71,7,81,3,93,307,11,3,7,31,7,47,9,53,9,67,73,9
%N 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.
%C A335301 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.
%C A335301 This sequence has similarities with A274206; here we consider consecutive prime numbers, there consecutive nonnegative integers.
%C A335301 There are no two consecutive equal terms.
%H A335301 Rémy Sigrist, <a href="/A335301/b335301.txt">Table of n, a(n) for n = 1..10000</a>
%F A335301 a(n) <= prime(n+1) with equality iff prime(n+1) is the least prime number with its number of digits and leading digit.
%e A335301 For n = 42:
%e A335301 - prime(42) = 181 and prime(43) = 191,
%e A335301 - floor(181/(10^1)) = 18 <> 19 = floor(191/(10^1)),
%e A335301 - floor(181/(10^2)) = 1 = floor(191/(10^2)),
%e A335301 - so a(42) = 191 mod (10^2) = 91.
%o A335301 (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))) }
%Y A335301 Cf. A274206, A335302 (binary variant).
%K A335301 nonn,base
%O A335301 1,1
%A A335301 _Rémy Sigrist_, May 31 2020