A279027 -id:A279027 - cp's OEIS frontend

A280667 a(n) = number of primes of the form 4k + 1 such that 2n - 4k - 1 is prime.

0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 2, 3, 1, 2, 2, 2, 3, 4, 0, 3, 4, 3, 4, 5, 2, 3, 4, 3, 5, 6, 0, 5, 6, 2, 4, 6, 3, 5, 6, 4, 3, 8, 2, 4, 6, 4, 4, 7, 2, 6, 8, 5, 5, 8, 4, 7, 10, 6, 6, 12, 3, 5, 10, 3, 6, 9, 4, 5, 6, 7, 8, 11, 3, 5, 10, 4, 8, 11, 2, 8, 10, 5, 6, 13, 6, 6, 8, 7, 7, 14, 2, 8, 12, 5

Offset: 1

Juri-Stepan Gerasimov, Jan 07 2017

nonn

Primes p such that a(p) = 0: 2, 3, 7, 19, 31.

			a(8) = 2 because 2*8 - 4*1 - 1 = 11 is prime where 4*1 + 1 = 5 is prime of the form 4k+1 and 2*8 - 4*3 - 1 = 3 is prime where 4*3 + 1 = 13 is prime of the form 4k+1.

Cf. A002144, A035026, A278287, A279027.

A280667 := func; [A280667(n):n in[1..100]];

a(n) = sum(k=1, 2*n, isprime(k) && isprime(2*n-k) && ((2*n-k) % 4 == 1)); \\ Michel Marcus, Jan 07 2017

A280616 Smallest m such that the m - s is a prime for exactly n distinct squarefree numbers s.

Original entry on oeis.org

3, 4, 9, 8, 16, 18, 26, 32, 24, 36, 42, 44, 48, 66, 70, 60, 74, 72, 94, 106, 84, 90, 102, 112, 130, 108, 126, 114, 166, 160, 150, 144, 184, 218, 174, 208, 168, 220, 138, 222, 232, 204, 216, 262, 302, 268, 234, 252, 246, 240, 264, 276, 306, 270, 340, 318, 294, 312, 342, 336, 406, 330, 324

Offset: 1

Juri-Stepan Gerasimov, Jan 06 2017

nonn

			a(1) = 3 because 3 - 1 = 2 is prime where 1 is squarefree number.
a(2) = 4 because 4 - 1 = 3 and 4 - 2 = 2 are primes where 1 and 2 are squarefree numbers.
a(3) = 9 because 9 - 2 = 7, 9 - 6 = 3, 9 - 7 = 2 are primes where 2, 6, 7 are squarefree numbers.

Cf. A004767, A005117, A098983, A279027.

cp's OEIS Frontend

A280667 a(n) = number of primes of the form 4k + 1 such that 2n - 4k - 1 is prime.

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