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 A072971 Least k such that the last digit of prime(n+k) = last digit of prime(n) in base 10. 2

%I #17 Mar 14 2021 18:42:13

%S 3,6,3,5,2,5,7,2,3,5,2,4,5,5,2,6,6,2,2,4,5,3,6,3,3,5,8,2,4,4,1,6,6,2,

%T 2,6,4,5,1,4,4,4,4,6,3,6,2,5,5,1,4,4,5,13,2,4,4,1,3,3,3,6,2,12,1,4,2,

%U 3,3,5,2,2,8,3,10,3,1,4,1,6,2,2,4,5,3,5,6,2,3,8,4,2,3,7,2,4,5,1,4,5,5,5,1

%N Least k such that the last digit of prime(n+k) = last digit of prime(n) in base 10.

%C Let S(n) = Sum_{k=4..n} a(k). Is the sequence of integers b(m) such that S(b(m)) > 4*b(m) finite? The first 3 terms are b(1)=794, b(2)=795, and b(3)= 1326. Is -4 <= 4*n-S(n) <= 13 always true? Is a(n) bounded?

%H Robert Israel, <a href="/A072971/b072971.txt">Table of n, a(n) for n = 4..10000</a>

%F Probably lim_{n -> infinity} S(n)/n = lim_{n -> infinity} (1/n)*Sum_{k=4..n} a(k) = 4.

%o (PARI) a(n)=if(n<0,0,k=1; while(abs(prime(k+n)%10-prime(n)%10)>0,k++); k)

%K base,easy,nonn

%O 4,1

%A _Benoit Cloitre_, Aug 13 2002

%E Edited by _Jon E. Schoenfield_, Jan 18 2020

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Last modified May 28 18:29 EDT 2023. Contains 363019 sequences. (Running on oeis4.)