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A305810 Filter sequence for a(Sophie Germain primes > 3) = constant sequences. 5
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 5, 22, 23, 24, 25, 26, 5, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 5, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 5, 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, 76, 77, 5, 78, 79, 80, 81, 82, 5, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Filer sequence for all such sequences S, for which S(A005384(k)) = constant for all k >= 3.

Restricted growth sequence transform of the ordered pair [A305900(n), A305901(1+n)].

For all i, j:

  a(i) = a(j) => A305900(i) = A305900(j),

  a(i) = a(j) => A305901(1+i) = A305901(1+j),

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

  a(i) = a(j) => A305985(i) = A305985(j).

LINKS

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

FORMULA

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

A305810(n) = if(n<5, n, if(A156660(n), 5, 3+n-A156874(n)));

CROSSREFS

Cf. A005384, A156660, A156874, A305900, A305901, A305978, A305985.

Sequence in context: A319717 A292266 A292267 * A171060 A254596 A286603

Adjacent sequences:  A305807 A305808 A305809 * A305811 A305812 A305813

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 16 2018

STATUS

approved

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Last modified October 14 16:48 EDT 2019. Contains 328022 sequences. (Running on oeis4.)