A244074 Odd integers m such that for every integer k>0, m*2^k-1 has a divisor in the set {3, 5, 7, 13, 37, 73, 109}.

1830187, 4643293, 17041931, 20787701, 50462309, 52363777, 66659587, 68026001, 71604733, 71817943, 88558303, 91609361, 93193151, 97363751, 118421557, 122606647, 123765359, 124808009, 131118733, 131408411, 134320001, 135411719, 139778591, 142339723

Offset

1,1

Comments

For n > 144, a(n) = a(n-144) + 803736570, the first 144 values are in the table.

It is enough to check k = 1..36 because 2^36 == 1 (mod 3*5*7*13*37*73*109). - Jason Yuen, Nov 21 2025

Links

Pierre CAMI, Table of n, a(n) for n = 1..144 (corrected by Jason Yuen)

Formula

For n > 144, a(n) = a(n-144) + 803736570.

Prog

(PARI) isok(m) = {if(m%2==0, return(0)); for(k=1, 36, if(gcd(m*2^k-1, 401868285)==1, return(0))); 1} \\ Jason Yuen, Nov 21 2025

Crossrefs

Cf. A076337, A244070, A244071, A244072, A244073, A244076.

Sequence in context: A147525 A205412 A249211 * A204951 A205639 A269117

Adjacent sequences: A244071 A244072 A244073 * A244075 A244076 A244077

Keyword

nonn

Author

Pierre CAMI, Jun 19 2014

Status

approved