cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A275989 a(n) = prime(prime(n)+1) - prime(n).

Original entry on oeis.org

3, 4, 8, 12, 26, 30, 44, 52, 66, 84, 100, 126, 140, 150, 176, 198, 222, 232, 270, 288, 300, 330, 350, 374, 424, 456, 466, 486, 492, 506, 592, 612, 650, 670, 714, 730, 772, 808, 830, 860, 890, 910, 972, 988, 1016, 1024, 1090, 1200, 1212, 1222, 1248, 1272, 1290, 1350, 1370, 1430, 1464
Offset: 1

Views

Author

Terry D. Grant, Aug 15 2016

Keywords

Examples

			For n=3, prime(prime(3)+1) = 13, and prime(3) = 5, therefore a(3) = 13 - 5 = 8.

Crossrefs

Cf. A072677, A008864, A168152, A275990.

Programs

  • Mathematica
    Table[Prime[Prime[n]+1] - Prime[n], {n, 1, 100}]
  • PARI
    a(n) = prime(prime(n)+1) - prime(n); \\ Michel Marcus, Aug 18 2016

Formula

a(n) = A000040(A008864(n)) - A000040(n) = A072677(n) - A000040(n).

A168247 Integers of the form (prime(p) - p)/10 for some prime p.

Original entry on oeis.org

1, 2, 6, 8, 12, 46, 48, 49, 71, 126, 147, 151, 162, 172, 189, 211, 223, 257, 272, 306, 309, 337, 347, 364, 382, 458, 495, 504, 525, 549, 550, 563, 596, 598, 615, 657, 664, 677, 685, 719, 720, 771, 824, 829, 862, 870, 892, 927, 954, 1052, 1065, 1069, 1083, 1097, 1099
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 21 2009

Keywords

Crossrefs

Cf. A168152.

Extensions

Removed split use of a variable in the definition; corrected a(4), inserted 151. - R. J. Mathar, Nov 23 2009

A378027 a(n) = prime(prime(prime(n))) - prime(prime(n)).

Original entry on oeis.org

2, 6, 20, 42, 96, 138, 218, 264, 348, 490, 582, 762, 884, 962, 1086, 1282, 1510, 1564, 1890, 2028, 2110, 2348, 2570, 2798, 3128, 3396, 3528, 3686, 3798, 3932, 4672, 4884, 5096, 5316, 5802, 5946, 6274, 6640, 6850, 7190, 7464, 7632, 8166, 8290, 8538, 8642, 9334, 10334, 10520, 10650, 10830, 11048, 11240, 11872, 12088, 12508
Offset: 1

Views

Author

Sean M. Drury, Nov 17 2024

Keywords

Examples

			For n=5, A038580(5)=127 and A006450(5)=31 so a(5) = 127 - 31 = 96.

Crossrefs

Cf. A000040, A006450, A038580, A014689, A168152.

Programs

  • Maple
    a:= ithprime@@3-ithprime@@2:
seq(a(n), n=1..56);  # Alois P. Heinz, Nov 18 2024
  • Mathematica
    Nest[Prime, Range[100], 3] - PrimePi /@ Nest[Prime, Range[100], 3]
  • PARI
    a(n) = my(q=prime(prime(n))); prime(q) - q; \\ Michel Marcus, Nov 18 2024

Formula

a(n) = A168152(prime(n)) = A014689(prime(prime(n))).
a(n) = A038580(n) - A006450(n).
a(n) ~ n*(log(n))^3.
a(n) == 0 (mod 2).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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