A305894 Filter sequence for a(Sophie Germain primes) = constant sequences.

1, 2, 2, 3, 2, 4, 5, 6, 7, 8, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 20, 21, 22, 23, 24, 2, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 2, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 2, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 2, 76, 77, 78, 79, 80, 2, 81

Offset

1,2

Comments

For all i, j:

a(i) = a(j) => A305800(i) = A305800(j),

a(i) = a(j) => A305978(i) = A305978(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Formula

a(1) = 1; for n > 1, a(n) = 2 if A156660(n) == 1 [when n is in A005384 = 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, ...], otherwise a(n) = 1+n-A156874(n).

Prog

(PARI)
up_to = 100000;
A156660(n) = (isprime(n)&&isprime(2*n+1)); \\ From A156660
partialsums(f, up_to) = { my(v = vector(up_to), s=0); for(i=1, up_to, s += f(i); v[i] = s); (v); }
v156874 = partialsums(A156660, up_to);
A156874(n) = v156874[n];
A305894(n) = if(n<2, n, if(A156660(n), 2, 1+n-A156874(n)));

Crossrefs

Cf. A005384, A156660, A156874, A305800, A305810, A305978.

Sequence in context: A305978 A305985 A319706 * A305811 A239471 A241509

Adjacent sequences: A305891 A305892 A305893 * A305895 A305896 A305897

Keyword

nonn

Author

Antti Karttunen, Jul 01 2018

Status

approved