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A246362 Numbers n such that if 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). 11
4, 6, 7, 9, 10, 12, 15, 16, 19, 20, 21, 22, 24, 27, 29, 30, 31, 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, 96, 97, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that A064216(n) > n.

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

The sequence grows as:

      a(100) = 148

     a(1000) = 1449

    a(10000) = 14264

   a(100000) = 141259

  a(1000000) = 1418197

and the powers of 10 occur at:

        a(5) = 10

       a(63) = 100

      a(701) = 1000

     a(6973) = 10000

    a(70845) = 100000

   a(705313) = 1000000

suggesting that the ratio a(n)/n is converging to a constant and an arbitrary natural number is more than twice as likely to be here than in the complement A246361. Compare this to the ratio present in the "inverse" case A246282.

LINKS

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

EXAMPLE

4 is present, as 2*4 - 1 = 7 = p_4, and p_{4-1} = p_3 = 5 > 4.

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.

35 is present, as 2*35 - 1 = 69 = 3*23 = p_2 * p_9, and p_1 * p_8 = 2*19 = 38 > 35.

PROG

(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);

isA246362(n) = (A064216(n) > n);

n = 0; i = 0; while(i < 10000, n++; if(isA246362(n), i++; write("b246362.txt", i, " ", n)));

(Scheme, with Antti Karttunen's IntSeq-library)

(define A246362 (MATCHING-POS 1 1 (lambda (n) (> (A064216 n) n))))

CROSSREFS

Complement: A246361.

Setwise difference of A246372 and A048674.

Cf. A000040, A064216, A064989, A246282.

Sequence in context: A104425 A174258 A080746 * A069909 A189715 A101993

Adjacent sequences:  A246359 A246360 A246361 * A246363 A246364 A246365

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 24 2014

STATUS

approved

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Last modified November 22 06:26 EST 2019. Contains 329389 sequences. (Running on oeis4.)