A246281 - OEIS

1, 2, 3, 5, 7, 11, 13, 17, 19, 22, 23, 25, 26, 29, 31, 33, 34, 37, 38, 41, 43, 46, 47, 51, 53, 55, 58, 59, 61, 62, 65, 67, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118, 119, 121, 122, 123, 127, 129, 131, 133, 134, 137, 139

COMMENTS

Numbers n such that A003961(n) < 2*n.

Numbers n such that A048673(n) <= n.

All primes (A000040) are members. (Cf. Bertrand's postulate).

EXAMPLE

1 is present, as 1 = empty product and 1 < 2.

2 = p_1 is in the sequence, as p_2 = 3 and 3/2 < 2.

4 = p_1 * p_1 is not a member, as p_2 * p_2 = 3*3 = 9, and 9/4 > 2.

22 = 2*11 = p_1 * p_5 is a member, as p_2 * p_6 = 39, and 39/22 < 2.

PROG

(PARI)

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f);

isA246281(n) = (A003961(n) < (n+n));

n = 0; i = 0; while(i < 10000, n++; if(isA246281(n), i++; write("b246281.txt", i, " ", n)));

(Scheme)

(define A246281 (MATCHING-POS 1 1 (lambda (n) (<= (A048673 n) n))))

CROSSREFS

Positions of negative terms in A252748.

EXTENSIONS

A new shorter version of name prepended by Antti Karttunen, Aug 27 2020