A246372 Numbers n such that 2n-1 = product_{k >= 1} (p_k)^(c_k), then n <= product_{k >= 1} (p_{k-1})^(c_k), where p_k indicates the k-th prime, A000040(k).

1, 2, 3, 4, 6, 7, 9, 10, 12, 15, 16, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 33, 34, 35, 36, 37, 40, 42, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 60, 62, 64, 65, 66, 67, 69, 70, 71, 72, 75, 76, 78, 79, 80, 81, 82, 84, 85, 87, 89, 90, 91, 92, 93, 96, 97, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110

Offset: 1

Author

Antti Karttunen, Aug 24 2014

Keywords

• nonn

Comments

Numbers n such that A064216(n) >= n.

Numbers n such that A064989(2n-1) >= n.

Examples

			1 is present, as 2*1 - 1 = empty product = 1.
2 is present, as 2*2 - 1 = 3 = p_2, and p_{2-1} = p_1 = 2 >= 2.
3 is present, as 2*3 - 1 = 5 = p_3, and p_{3-1} = p_2 = 3 >= 3.
5 is not present, as 2*5 - 1 = 9 = p_2 * p_2, and p_1 * p_1 = 4, with 4 < 5.
6 is present, as 2*6 - 1 = 11 = p_5, and p_{5-1} = p_4 = 7 >= 6.
25 is present, as 2*25 - 1 = 49 = p_4^2, and p_3^2 = 5*5 = 25 >= 25.
35 is present, as 2*35 - 1 = 69 = 3*23 = p_2 * p_9, and p_1 * p_8 = 2*19 = 38 >= 35.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Complement: A246371

Union of A246362 and A048674.

Subsequences: A006254 (A111333), A246373 (the primes present in this sequence).

Cf. A000040, A064216, A064989, A246352.

Programs

PARI

default(primelimit, 2^30);
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A064216(n) = A064989((2*n)-1);
isA246372(n) = (A064216(n) >= n);
n = 0; i = 0; while(i < 10000, n++; if(isA246372(n), i++; write("b246372.txt", i, " ", n)));
(Scheme, with Antti Karttunen's IntSeq-library)
(define A246372 (MATCHING-POS 1 1 (lambda (n) (>= (A064216 n) n))))