A244562 -id:A244562 - cp's OEIS frontend

A244563 Odd integers n such that for every integer k>0, n*2^k+1 has a divisor in the set { 3, 5, 7, 13, 19, 37, 109 }.

1290677, 4095859, 5841947, 7158107, 8959163, 9044629, 9252323, 9933857, 10306187, 11000303, 15598231, 16010419, 16625747, 16907749, 18068693, 19428919, 20189993, 23487497, 25614893, 26471633, 28410121, 30375901, 30666137, 32552687

Offset: 1

Pierre CAMI, Jun 30 2014

nonn

For n > 144 a(n) = a(n-144) + 209191710, the first 144 values are in the table.

Pierre CAMI, Table of n, a(n) for n = 1..144

Cf. A076336, A244072, A244561, A244562.

For n > 144 a(n) = a(n-144) + 209191710.

A244564 Odd integers n such that for every integer k>0, n * 2^k + 1 has a divisor in the set { 3, 5, 7, 13, 19, 73, 109 }.

Original entry on oeis.org

934909, 1259779, 6828631, 11822359, 12151397, 15285707, 17220887, 23277113, 25912463, 32971909, 34689511, 38206517, 38257411, 45181667, 46337843, 48339497, 57410477, 63676073, 67510217, 68468753, 68708387, 69169397, 70312793, 71151293

Offset: 1

Pierre CAMI, Jun 30 2014

nonn

For n > 144, a(n) = a(n-144) + 412729590, the first 144 values are in the table.

Pierre CAMI, Table of n, a(n) for n = 1..144

Cf. A076336, A244073, A244561, A244562, A244563.

For n > 144, a(n) = a(n-144) + 412729590.

A244565 Odd integers n such that for every integer k>0, n*2^k+1 has a divisor in the set { 3, 5, 7, 13, 37, 73, 109 }.

Original entry on oeis.org

322523, 12413281, 16921847, 27862127, 29095681, 35430841, 43925747, 47635073, 50273851, 56517767, 57816799, 59929127, 60666107, 63662611, 66887071, 69265069, 77564731, 83460571, 87376127, 104697533

Offset: 1

Pierre CAMI, Jun 30 2014

nonn

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

Pierre CAMI, Table of n, a(n) for n = 1..144

Cf. A076336, A244074, A244561, A244562, A244563, A244564.

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

A305473 Let k be a Sierpiński or Riesel number divisible by 2n - 1, and let p be the largest number in a set of primes which cover every number of the form k2^m + 1 (or of the form k*2^m - 1) with m >= 1. a(n) = p if and only if there exists no number k that has a covering set with largest prime < p.

Original entry on oeis.org

73, 257, 151, 151, 257, 73, 151, 1321, 73, 109, 1321, 73, 151, 257, 73, 73, 331, 257, 109, 331, 73, 73, 1321, 73, 151, 331, 73, 241

Offset: 1

Arkadiusz Wesolowski, Jun 02 2018

nonn

R. G. Stanton found that a(2) = 257.
a(n) >= 73 for any n, see [Stanton].
There exist infinitely many Riesel numbers that are divisible by 15. The number 334437671621489828385689959795356586832846847109919809460835 is one such number.

			Examples of the covering sets:
- for n = 2, the set is {5, 7, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257},
- for n = 3, the set is {3, 7, 11, 13, 19, 31, 37, 41, 61, 73, 109, 151},
- for n = 4, the set is {3, 5, 11, 13, 19, 31, 37, 41, 61, 73, 151},
- for n = 6, the set is {3, 5, 7, 13, 19, 37, 73},
- for n = 7, the set is {3, 5, 7, 11, 19, 31, 37, 41, 61, 73, 151},
- for n = 8, the set is {7, 11, 13, 17, 19, 29, 31, 37, 41, 43, 61, 71, 73, 97, 109, 113, 127, 151, 193, 211, 241, 257, 281, 331, 337, 421, 433, 577, 673, 1153, 1321},
- for n = 11, the set is {5, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 181, 193, 241, 257, 331, 433, 577, 631, 673, 1153, 1321},
- for n = 17, the set is {5, 7, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257, 331},
- for n = 18, the set is {3, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257},
- for n = 20, the set is {5, 7, 11, 17, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257, 331},
- for n = 26, the set is {5, 7, 11, 13, 19, 31, 37, 41, 61, 73, 97, 109, 151, 241, 257, 331},
- for n = 28, the set is {3, 7, 13, 17, 19, 37, 73, 109, 241}.

R. G. Stanton, Further results on covering integers of the form 1 + k * 2^n by primes, pp. 107-114 in: Kevin L. McAvaney (ed.), Combinatorial Mathematics VIII, Lecture Notes in Mathematics 884, Berlin: Springer, 1981.

Carlos Rivera, Problem 49. Sierpinski-like numbers, The Prime Puzzles and Problems Connection.

Cf. A076336, A101036, A187714, A187716, A213529, A222534, A244071, A244562, A306151.

a(((2*n-1)^b+1)/2) = a(n) for every b >= 2.
a((2*b-1)*n-b+1) >= a(n) for every b >= 2; n > 1.
a(n) = 73 if and only if gcd(2*n-1, 70050435) = 1.

A244566 Odd integers n such that for every integer k>0, n*2^k+1 has a divisor in the set { 3, 5, 7, 13, 17, 97, 257 }.

Original entry on oeis.org

327739, 5455789, 8879993, 9043831, 21823667, 25763447, 29949559, 75037639, 92732027, 119863547, 119879899, 122091961, 146880319, 151060223, 152106751, 163378771, 181339441, 182384417, 182646049, 218039041, 232190537

Offset: 1

Pierre CAMI, Jun 30 2014

These are the Sierpiński numbers (A076336) with covering set {3, 5, 7, 13, 17, 97, 257}. - David W. Wilson, Jul 18 2014

For n > 96, a(n) = a(n-96) + 1156954890, the first 96 values are in the table.

Pierre CAMI, Table of n, a(n) for n = 1..96

Cf. A076336, A244076, A244561, A244562, A244563, A244564, A244565.

is(n)=my(G=578477445,t=Mod(n,G)); for(k=1,768,t*=2; if(gcd(t+1, G)==1, return(0))); n%2 \\ Charles R Greathouse IV, Jul 18 2014

For n > 96, a(n) = a(n-96) + 1156954890.

cp's OEIS Frontend

A244563 Odd integers n such that for every integer k>0, n*2^k+1 has a divisor in the set { 3, 5, 7, 13, 19, 37, 109 }.

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A244564 Odd integers n such that for every integer k>0, n * 2^k + 1 has a divisor in the set { 3, 5, 7, 13, 19, 73, 109 }.

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A244565 Odd integers n such that for every integer k>0, n*2^k+1 has a divisor in the set { 3, 5, 7, 13, 37, 73, 109 }.

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A244566 Odd integers n such that for every integer k>0, n*2^k+1 has a divisor in the set { 3, 5, 7, 13, 17, 97, 257 }.

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