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

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, 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, 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

Offset

4,1

Comments

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?

Links

Robert Israel, Table of n, a(n) for n = 4..10000

Formula

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

Prog

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

Crossrefs

Sequence in context: A111762 A185582 A201398 * A256681 A340704 A199951

Adjacent sequences: A072968 A072969 A072970 * A072972 A072973 A072974

Keyword

base,easy,nonn

Author

Benoit Cloitre, Aug 13 2002

Extensions

Edited by Jon E. Schoenfield, Jan 18 2020

Status

approved