A113396 -id:A113396 - cp's OEIS frontend

A113397 What are the values of k in the term Prime(n+1)^2-Prime(n)^2 = a+k*(Prime(n+1)) if "a" is element of {0,1,...,Prime(n+1)-1}.

1, 3, 3, 6, 3, 7, 3, 7, 10, 3, 11, 7, 3, 7, 11, 11, 3, 11, 7, 3, 11, 7, 11, 15, 7, 3, 7, 3, 7, 26, 7, 11, 3, 19, 3, 11, 11, 7, 11, 11, 3, 19, 3, 7, 3, 23, 23, 7, 3, 7, 11, 3, 19

Offset: 1

Marian Kraus, Oct 26 2005

nonn

			3^2-2^2=2+1*3; 5^2-3^2=1+3*5; 7^2-5^2=3+3*7; 11^2-7^2=6+6*11; 13^2-11^2=9+3*13; etc.

Cf. A113396.

Prime(n+1)^2-Prime(n)^2 = a+k*(Prime(n+1)) "a" element of {0, 1, ..., Prime(n+1)-1}

A113398 How many times did the value of k appear at the previous primes including the n-th one? (Prime(n+1))^2-(Prime(n))^2 = a+k*(Prime(n+1)) if a is element of {0,1,...,Prime(n+1)-1}.

Original entry on oeis.org

1, 1, 2, 1, 3, 1, 4, 2, 1, 5, 1, 3, 6, 4, 2, 3, 7, 4, 5, 8, 5, 6, 6, 1, 7, 9, 8, 10, 9, 1, 10, 7, 11, 1, 12, 8, 9, 11, 10, 11, 13, 2, 14, 12, 15, 1, 2, 13, 16, 14, 12, 17, 3

Offset: 1

Marian Kraus, Oct 26 2005

nonn

			3^2-2^2 = 2+1*3 (first "1"); 5^2-3^2 = 1+3*5 (first "3"); 7^2-5^2 = 3+3*7 (2nd "3");
11^2-7^2 = 6+6*11 (first "6"); 13^2-11^2 = 9+3*13 (3rd "3"); etc.

Cf. A113396, A113397.

cp's OEIS Frontend

A113397 What are the values of k in the term Prime(n+1)^2-Prime(n)^2 = a+k*(Prime(n+1)) if "a" is element of {0,1,...,Prime(n+1)-1}.

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