A061414 -id:A061414 - cp's OEIS frontend

A061415 Coefficient values m resulting from A061414.

5, 7, 1, 13, 22, 11, 3, 25, 8, 3, 63, 63, 15, 64, 32, 8, 18, 9, 45, 90, 95, 115, 110, 11, 75, 17, 145, 28, 14, 131, 160, 102, 166, 169, 229, 62, 149, 184, 5, 140, 70, 165, 255, 98, 181, 9, 228, 114, 57, 33, 199, 200, 297, 330, 144, 72, 18, 9, 17, 195, 129, 273, 384, 24

Offset: 1

Patrick De Geest, May 15 2001

nonn

			a(1) = 5 since 5*2^A061414(1) - 1 = 5*2^8 - 1 = 1279 is prime.
a(2) = 7 since 7*2^A061414(2) - 1 = 7*2^9 - 1 = 3583 is prime.

Cf. A061410-A061414.

Offset changed by Andrew Howroyd, Aug 13 2024

A061410 Numbers k such that m*2^k+1 is not prime for all coefficients m in the range 0<=m<=k.

Original entry on oeis.org

9, 10, 22, 31, 86, 99, 100, 101, 113, 114, 115, 130, 135, 136, 149, 154, 169, 217, 218, 223, 224, 283, 301, 309, 358, 383, 384, 422, 423, 424, 425, 426, 449, 457, 473, 495, 505, 506, 541, 542, 548, 549, 564, 571, 572, 573, 628, 668, 670, 681, 682, 683, 713

Offset: 1

Patrick De Geest, May 15 2001

nonn

Robert Israel, Table of n, a(n) for n = 1..285

Cf. A061411, A061412, A061413, A061414, A061415.

filter:= n -> andmap(not isprime, [seq(m*2^n+1,m=1..n)]):
select(filter, [$1..1000]); # Robert Israel, Dec 10 2017

okQ[n_] := AllTrue[2^n Range[n] + 1, CompositeQ];
Select[Range[1000], okQ] (* Jean-François Alcover, Mar 25 2019 *)

isok(n) = {for (m=0, n, if (isprime(m*2^n+1), return (0));); return (1);} \\ Michel Marcus, Dec 11 2017

A061411 Numbers k such that m*2^k - 1 is nonprime for all coefficients m in the range 0 <= m <= k.

Original entry on oeis.org

1, 22, 24, 65, 110, 112, 135, 137, 166, 167, 218, 219, 220, 228, 229, 239, 257, 280, 310, 344, 345, 346, 398, 399, 403, 404, 405, 430, 439, 440, 475, 494, 504, 505, 508, 522, 524, 534, 535, 536, 557, 559, 592, 619, 620, 624, 625, 626, 679, 703, 705, 706

Offset: 1

Patrick De Geest, May 15 2001

nonn

Cf. A061410, A061412, A061413, A061414, A061415.

Name edited and Offset changed by Jon E. Schoenfield, Oct 26 2019

A061412 Numbers k such that m*2^k + 1 is prime for exactly one coefficient m in the range 0 <= m <= k.

Original entry on oeis.org

1, 2, 3, 4, 5, 18, 21, 23, 24, 26, 30, 32, 34, 35, 56, 57, 58, 59, 69, 70, 71, 87, 95, 96, 97, 106, 107, 108, 109, 112, 116, 120, 121, 131, 137, 139, 140, 142, 150, 151, 156, 159, 161, 163, 171, 172, 176, 177, 178, 181, 191, 192, 194, 195, 196, 197, 212, 219, 220

Offset: 1

Patrick De Geest, May 15 2001

nonn

For corresponding coefficient values see A061413.

Cf. A061410, A061411, A061413, A061414, A061415.

Name edited and Offset changed by Jon E. Schoenfield, Oct 26 2019

A382447 Number of positive k <= n such that k*2^n - 1 is prime.

Original entry on oeis.org

0, 2, 2, 2, 2, 3, 2, 1, 1, 3, 3, 2, 3, 2, 2, 4, 6, 3, 1, 3, 3, 0, 1, 0, 1, 1, 2, 3, 2, 3, 4, 2, 2, 1, 5, 2, 4, 2, 1, 3, 4, 3, 4, 2, 2, 3, 2, 3, 2, 3, 3, 3, 4, 5, 2, 2, 3, 1, 3, 3, 3, 4, 3, 1, 0, 1, 2, 1, 4, 3, 3, 5, 3, 3, 6, 2, 3, 3, 3, 2, 3, 1, 1, 1, 3, 1, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 3, 3, 2

Offset: 1

Juri-Stepan Gerasimov, Mar 26 2025

nonn

Cf. A002234, A003261, A382119.

Cf. A061411 (indices of 0s), A061414 (indices of 1s).

[#[k: k in [1..n] | IsPrime(k*2^n-1)]: n in [1..100]];

a[n_]:=Length[Select[Range[n],PrimeQ[#*2^n-1] &]]; Array[a,100] (* Stefano Spezia, Mar 26 2025 *)

cp's OEIS Frontend

A061415 Coefficient values m resulting from A061414.

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A061410 Numbers k such that m*2^k+1 is not prime for all coefficients m in the range 0<=m<=k.

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Maple

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A061411 Numbers k such that m*2^k - 1 is nonprime for all coefficients m in the range 0 <= m <= k.

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A061412 Numbers k such that m*2^k + 1 is prime for exactly one coefficient m in the range 0 <= m <= k.

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A382447 Number of positive k <= n such that k*2^n - 1 is prime.

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Magma

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