A180247 -id:A180247 - cp's OEIS frontend

A194607 Record values in A194606.

0, 1, 2, 4, 5, 6, 11, 17, 20, 28, 70, 99, 150, 726, 7431, 22394, 85461, 191207

Offset: 1

Arkadiusz Wesolowski, Aug 30 2011

The index sequence of this one is 1, 3, 6, 15, 17, 29, 53, 115, 186, 220, 229, 1886, 5344, 5736, 66774, 1087403, 14747671, 158018119.

a(17) was found in 2000 by Wilfrid Keller and a(18) was found in 2003 by Patrick De Geest.

			A194606(53) = 11 since A194606(115) = 17 is the next record value.

Wilfrid Keller, personal communication, 2010.

Chris K. Caldwell, The List of Largest Known Primes, 270704167 * 2^85461 - 1
Chris K. Caldwell, The List of Largest Known Primes, 3296757029 * 2^191207 + 1
Carlos Rivera, Problem 30

Cf. A194591, A194600, A194603, A194606, A194608, A194635, A194636, A194637, A194638, A194639.

Cf. A103963, A103964, A076335, A180247.

l = -1; Flatten[Table[p = Prime[n]; k = 0; While[! PrimeQ[p*2^k - 1] && ! PrimeQ[p*2^k + 1], k++]; If[k > l, l = k, {}], {n, 10^4}]] (* Arkadiusz Wesolowski, Sep 04 2011 *)

A194637 Record values in A194636.

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 11, 18, 20, 28, 70, 106, 150, 726, 2906, 7431, 14073, 22394, 41422, 82587, 85461, 356981

Offset: 1

Arkadiusz Wesolowski, Aug 31 2011

The index sequence is 1, 3, 7, 24, 30, 55, 121, 168, 555, 687, 724, 7447, 26134, 28272, 324802, 419221, 4420051, 8467881, 50302257, 59186640, 135352084, 677738616, ... given by formula (A194639(n)+1)/2.

			A194636(55) = 6 since A194636(121) = 11 is the next record value.

Wilfrid Keller, personal communication, 2010.

Chris K. Caldwell, The List of Largest Known Primes, 1355477231 * 2^356981 + 1
Carlos Rivera, Problem 30

Cf. A194591, A194600, A194603, A194606, A194607, A194608, A194635, A194636, A194638, A194639.

Cf. A103963, A103964, A076335, A180247.

l = -1; Flatten[Table[n = 2*n - 1; k = 0; While[! PrimeQ[n*2^k - 1] && ! PrimeQ[n*2^k + 1], k++]; If[k > l, l = k, {}], {n, 10^5}]] (* Arkadiusz Wesolowski, Sep 04 2011 *)

a(n) = A194591(A194639(n)) = A194636((A194639(n)+1)/2).

a(22) was found in 2002 by Wilfrid Keller.

A364413 Odd numbers m such that for every k >= 1, m*2^k + 1 has a divisor in the set {3, 7, 11, 19, 31, 37, 41, 61, 73, 109, 151, 331}.

Original entry on oeis.org

189035277393779, 212050850472529, 618127765127603, 777947701660121, 1171304921532749, 1358735367828947, 1834310020939021, 2357654372323739, 2638037471052913, 3025664372930897, 3935005074246167, 4688754513654559, 4996748200142999, 5425272498782051, 5455203077891285

Offset: 1

Arkadiusz Wesolowski, Jul 23 2023

nonn

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..34560

Cf. A076336, A076335, A180247, A291360, A364412.

For n > 34560, a(n) = a(n-34560) + 10014447295554878022.

A364412 Odd numbers m such that for every k >= 1, m*2^k - 1 has a divisor in the set {3, 7, 11, 19, 31, 37, 41, 61, 73, 109, 151, 331}.

Original entry on oeis.org

144323411864333, 175321252530209, 190779128601685, 316031956469111, 389882208980861, 450590081221877, 2420018284798363, 2715458757443051, 3161282469971861, 3366332338600025, 3643757921262355, 4380746955320089, 4409682697067321, 5089175909950511, 5281690092088615

Offset: 1

Arkadiusz Wesolowski, Jul 23 2023

nonn

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..34560

Cf. A101036, A076335, A180247, A291360, A364413.

For n > 34560, a(n) = a(n-34560) + 10014447295554878022.

A256237 Primes p such that for all 2^k < p the numbers p + 2^k, p - 2^k, p2^k + 1, and p2^k - 1 are composite.

Original entry on oeis.org

8923, 24943, 35437, 42533, 52783, 83437, 105953, 116437, 126631, 133241, 145589, 164729, 172331, 192173, 204013, 215279, 254329, 304709, 308899, 398833, 430499, 436687, 454351, 476869, 479909, 483443, 497597, 522479, 527729, 529103, 545257, 561439, 562651

Offset: 1

Arkadiusz Wesolowski, Mar 20 2015

nonn

Subsequence of A256163.

Cf. A006285, A065381, A153352, A180247, A255967.

lst:=[]; for p in [3..562651 by 2] do if IsPrime(p) then t:=0; k:=0; while 2^k lt p do if IsPrime(p-2^k) or IsPrime(p+2^k) or IsPrime(p*2^k-1) or IsPrime(p*2^k+1) then t:=1; break; end if; k+:=1; end while; if IsZero(t) then Append(~lst, p); end if; end if; end for; lst;

A263560 Primes p such that for every k >= 1, p*2^k + 1 has a divisor in the set {3, 5, 13, 17, 97, 241, 257}.

Original entry on oeis.org

37158601, 7425967459, 9013226179, 13671059747, 14140683563, 17190420571, 17210867747, 18553286303, 18563509891, 19720992901, 20064786439, 22400387281, 23728062893, 29428753891, 36195177107, 41074421693, 44786947187, 45199948253, 48845530249

Offset: 1

Arkadiusz Wesolowski, Oct 21 2015

nonn

What is the smallest term of this sequence that belongs to A180247? Is it the smallest prime Brier number?

Chris Caldwell, The Prime Glossary, Sierpinski number
Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comput. 29 (1975), pp. 79-81.
Carlos Rivera, Problem 52

Cf. A076336, A180247, A263562.

Subsequence of A263347.

A263562 Primes p such that for every k >= 1, p*2^k - 1 has a divisor in the set {3, 5, 13, 17, 97, 241, 257}.

Original entry on oeis.org

1865978047, 1889699677, 2362339121, 3637126963, 11776639499, 19321614419, 20000692169, 20111311169, 20592473107, 20597584901, 21477425107, 23368396573, 23479945327, 25326720611, 26161244323, 27190405961, 27380064223, 27474950743, 31467088979

Offset: 1

Arkadiusz Wesolowski, Oct 21 2015

nonn

What is the smallest term of this sequence that belongs to A180247? Is it the smallest prime Brier number?

Chris Caldwell, The Prime Glossary, Riesel number
Carlos Rivera, Problem 52

Cf. A101036, A180247, A263560.

Subsequence of A263561.

A263645 Primes that are neither of the form p + 2^k nor of the form p - 2^k with k > 0, and p prime.

Original entry on oeis.org

2, 52504261, 55414847, 79933129, 152485283, 166441831, 177702619, 197903207, 199013093, 220403959, 226794259, 230701763, 245215801, 266642731, 304921637, 321979283, 335035097, 355404353, 359018299, 369810769, 388048561, 412590797, 445661719, 506400173, 540426473

Offset: 1

Arkadiusz Wesolowski, Oct 22 2015

nonn

Primes p such that for all k > 0 the numbers p + 2^k and p - 2^k are nonprimes.

Except for 2, this sequence is the intersection of A065381 and A137715.

Cf. A065381, A137715, A153352, A180247, A263644.

cp's OEIS Frontend

A194607 Record values in A194606.

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A194637 Record values in A194636.

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A364413 Odd numbers m such that for every k >= 1, m*2^k + 1 has a divisor in the set {3, 7, 11, 19, 31, 37, 41, 61, 73, 109, 151, 331}.

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A364412 Odd numbers m such that for every k >= 1, m*2^k - 1 has a divisor in the set {3, 7, 11, 19, 31, 37, 41, 61, 73, 109, 151, 331}.

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A256237 Primes p such that for all 2^k < p the numbers p + 2^k, p - 2^k, p*2^k + 1, and p*2^k - 1 are composite.

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A263560 Primes p such that for every k >= 1, p*2^k + 1 has a divisor in the set {3, 5, 13, 17, 97, 241, 257}.

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A263562 Primes p such that for every k >= 1, p*2^k - 1 has a divisor in the set {3, 5, 13, 17, 97, 241, 257}.

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A263645 Primes that are neither of the form p + 2^k nor of the form p - 2^k with k > 0, and p prime.

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A256237 Primes p such that for all 2^k < p the numbers p + 2^k, p - 2^k, p2^k + 1, and p2^k - 1 are composite.