A063086 -id:A063086 - cp's OEIS frontend

A066940 Numbers k such that gcd(prime(k+1) + 1, prime(k) + 1) = 2.

2, 3, 5, 6, 7, 10, 11, 12, 13, 17, 18, 20, 21, 24, 25, 26, 28, 29, 30, 33, 35, 36, 37, 41, 42, 43, 44, 45, 49, 50, 52, 53, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 69, 70, 73, 74, 77, 78, 79, 81, 82, 83, 84, 87, 88, 89, 98, 99, 100, 101, 104, 105, 106, 109, 110, 111, 112, 113

Offset: 1

Benoit Cloitre, Jan 24 2002

nonn

Numbers k such that A063086(k) = 2. - Andrew Howroyd, Dec 10 2024

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A063086, A066941, A066942, A066943, A066944, A067603, A067604.

Select[ Range[120], GCD[ Prime[ # + 1] + 1, Prime[ # ] + 1] == 2 & ]

isok(k) = { gcd(prime(k+1) + 1, prime(k) + 1) == 2 } \\ Harry J. Smith, Apr 09 2010

Edited by Robert G. Wilson v, Feb 01 2002

A066941 Numbers k such that gcd(prime(k+1) + 1, prime(k) + 1) = 4.

Original entry on oeis.org

4, 8, 14, 19, 22, 27, 31, 38, 46, 47, 48, 63, 75, 85, 90, 93, 94, 95, 114, 117, 124, 131, 143, 149, 153, 154, 155, 163, 181, 192, 207, 213, 224, 229, 232, 235, 241, 242, 247, 248, 249, 261, 276, 285, 299, 303, 304, 314, 327, 328, 333, 334, 335, 348, 364, 370

Offset: 1

Benoit Cloitre, Jan 24 2002

nonn

Numbers k such that A063086(k) = 4. - Andrew Howroyd, Dec 10 2024

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A063086, A066940, A066942, A066943, A066944, A067603, A067604.

Select[ Range[400], GCD[ Prime[ # + 1] + 1, Prime[ # ] + 1] == 4 & ]

isok(k) = { gcd(prime(k+1) + 1, prime(k) + 1) == 4 } \\ Harry J. Smith, Apr 10 2010

Edited by Robert G. Wilson v, Feb 01 2002

A066942 Numbers k such that gcd(prime(k+1) + 1, prime(k) + 1) = 6.

Original entry on oeis.org

9, 15, 16, 23, 32, 39, 40, 51, 54, 55, 56, 71, 76, 86, 96, 97, 102, 103, 107, 108, 118, 119, 123, 139, 160, 161, 164, 165, 170, 184, 185, 194, 195, 199, 200, 208, 218, 219, 227, 238, 245, 252, 255, 267, 290, 291, 292, 293, 298, 311, 312, 329, 342, 345, 349

Offset: 1

Benoit Cloitre, Jan 24 2002

nonn

Numbers k such that A063086(k) = 6. - Andrew Howroyd, Dec 10 2024

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A063086, A066940, A066941, A066943, A066944, A067603, A067604.

Select[ Range[400], GCD[ Prime[ # + 1] + 1, Prime[ # ] + 1] == 6 & ]
Drop[Position[Partition[Prime[Range[400]],2,1],?(GCD@@(#+1)==6&)],2]//Flatten (* _Harvey P. Dale, Nov 08 2022 *)

isok(k) = { gcd(prime(k+1) + 1, prime(k) + 1) == 6 } \\ Harry J. Smith, Apr 10 2010

Edited by Robert G. Wilson v, Feb 01 2002

A066943 Numbers k such that gcd(prime(k+1) + 1, prime(k) + 1) = 8.

Original entry on oeis.org

72, 92, 128, 132, 156, 166, 228, 246, 281, 282, 386, 417, 507, 519, 619, 620, 640, 641, 661, 712, 738, 739, 759, 801, 853, 898, 915, 1000, 1077, 1152, 1241, 1246, 1273, 1289, 1297, 1364, 1389, 1421, 1489, 1493, 1525, 1543, 1564, 1632, 1691, 1699, 1729

Offset: 1

Benoit Cloitre, Jan 24 2002

nonn

Numbers k such that A063086(k) = 8. - Andrew Howroyd, Dec 10 2024

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A063086, A066940, A066941, A066942, A066944, A067603, A067604.

Select[ Range[120], GCD[ Prime[ # + 1] + 1, Prime[ # ] + 1] == 8 & ]

isok(k) = { gcd(prime(k+1) + 1, prime(k) + 1) == 8 } \\ Harry J. Smith, Apr 10 2010

Edited by Robert G. Wilson v, Feb 01 2002

A066944 Numbers k such that gcd(prime(k+1) + 1, prime(k) + 1) = 10.

Original entry on oeis.org

34, 80, 127, 145, 157, 175, 204, 222, 266, 289, 308, 316, 397, 442, 443, 518, 525, 578, 593, 656, 690, 746, 757, 773, 793, 832, 861, 866, 892, 908, 923, 949, 958, 971, 985, 1013, 1029, 1051, 1071, 1102, 1125, 1195, 1236, 1314, 1329, 1340, 1350, 1403, 1434

Offset: 1

Benoit Cloitre, Jan 24 2002

nonn

Numbers k such that A063086(k) = 10. - Andrew Howroyd, Dec 10 2024

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A063086, A066940, A066941, A066942, A066943, A067603, A067604.

Select[ Range[1500], GCD[ Prime[ # + 1] + 1, Prime[ # ] + 1] == 10 & ]
PrimePi/@Select[Partition[Prime[Range[1500]],2,1],GCD@@(#+1)==10&][[All,1]] (* Harvey P. Dale, May 05 2018 *)

isok(k) = { gcd(prime(k+1) + 1, prime(k) + 1) == 10 } \\ Harry J. Smith, Apr 10 2010

Edited by Robert G. Wilson v, Feb 01 2002

A309772 Least common multiple of prime(n+1)+1 and prime(n)+1.

Original entry on oeis.org

12, 12, 24, 24, 84, 126, 180, 120, 120, 480, 608, 798, 924, 528, 432, 540, 1860, 2108, 1224, 2664, 2960, 1680, 1260, 4410, 4998, 5304, 2808, 5940, 6270, 7296, 4224, 3036, 9660, 2100, 11400, 12008, 12956, 6888, 4872, 5220, 16380, 17472, 18624, 19206, 19800, 10600

Offset: 1

Daniel Hoyt, Aug 16 2019

a(n) = (prime(n)+1)*(prime(n+1)+1)/2 if n is in A066940. - Robert Israel, Aug 16 2019

Daniel Hoyt, Table of n, a(n) for n = 1..1000

Cf. A008864, A063086 (gcd), A066940, A180617 (product).

[Lcm(1+NthPrime(n),1+NthPrime(n+1)):n in [1..50]]; // Marius A. Burtea, Aug 16 2019

P:= [seq(ithprime(i),i=1..100)]:
seq(ilcm(P[i]+1,P[i+1]+1),i=1..99); # Robert Israel, Aug 16 2019

Array[LCM[Prime[#] + 1, Prime[# + 1] + 1] &, 50] (* Amiram Eldar, Aug 16 2019 *)

a(n) = lcm(A008864(n+1), A008864(n)) = lcm(prime(n+1)+1, prime(n)+1).

cp's OEIS Frontend

A066940 Numbers k such that gcd(prime(k+1) + 1, prime(k) + 1) = 2.

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A066941 Numbers k such that gcd(prime(k+1) + 1, prime(k) + 1) = 4.

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A066942 Numbers k such that gcd(prime(k+1) + 1, prime(k) + 1) = 6.

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A066943 Numbers k such that gcd(prime(k+1) + 1, prime(k) + 1) = 8.

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A066944 Numbers k such that gcd(prime(k+1) + 1, prime(k) + 1) = 10.

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A309772 Least common multiple of prime(n+1)+1 and prime(n)+1.

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