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A246361 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). 12
1, 2, 3, 5, 8, 11, 13, 14, 17, 18, 23, 25, 26, 28, 32, 33, 38, 39, 41, 43, 50, 53, 58, 59, 61, 63, 68, 73, 74, 77, 83, 86, 88, 93, 94, 95, 98, 104, 113, 116, 122, 123, 128, 131, 137, 138, 140, 143, 149, 158, 163, 167, 172, 173, 176, 179, 182, 185, 188, 193, 194, 200, 203, 212, 213, 215, 218, 221, 228, 230, 233 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

The sequence grows as:

      a(100) = 332

     a(1000) = 3207

    a(10000) = 34213

   a(100000) = 340703

  a(1000000) = 3388490

suggesting that overall, less than one third of natural numbers appear in this sequence, and more than two thirds in the complement, A246362. See also comments in the latter.

LINKS

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

EXAMPLE

1 is present, as 2*1 - 1 = empty product = 1.

12 is not present, as (2*12)-1 = 23 = p_9, and p_8 = 19, with 12 < 19.

14 is present, as (2*14)-1 = 27 = p_2^3 = 8, and 14 >= 8.

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);

isA246361(n) = (A064216(n) <= n);

n = 0; i = 0; while(i < 10000, n++; if(isA246361(n), i++; write("b246361.txt", i, " ", n)));

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

(define A246361 (MATCHING-POS 1 1 (lambda (n) (<= (A064216 n) n))))

CROSSREFS

Complement: A246362.

Union of A246371 and A048674.

Subsequence: A246360.

Cf. A000040, A064216, A064989, A246281.

Sequence in context: A298205 A117725 A106637 * A228855 A171048 A209292

Adjacent sequences:  A246358 A246359 A246360 * A246362 A246363 A246364

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 24 2014

STATUS

approved

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Last modified November 14 02:19 EST 2019. Contains 329108 sequences. (Running on oeis4.)