A123134 -id:A123134 - cp's OEIS frontend

A286623 Square array A(n,k) = A276943(n,k)/A002110(n-1), read by descending antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

1, 3, 1, 4, 4, 1, 5, 6, 6, 1, 7, 7, 10, 8, 1, 9, 16, 11, 14, 12, 1, 10, 19, 36, 15, 22, 14, 1, 11, 21, 41, 78, 23, 26, 18, 1, 13, 22, 45, 85, 144, 27, 34, 20, 1, 15, 31, 46, 91, 155, 222, 35, 38, 24, 1, 16, 34, 71, 92, 165, 235, 324, 39, 46, 30, 1, 17, 36, 76, 155, 166, 247, 341, 438, 47, 58, 32, 1, 18, 37, 80, 162, 287, 248, 357, 457, 668, 59, 62, 38, 1

Offset: 1

Antti Karttunen, Jun 28 2017

			The top left 12 X 12 corner of the array:
  1,  3,  4,  5,    7,    9,   10,   11,   13,   15,   16,   17
  1,  4,  6,  7,   16,   19,   21,   22,   31,   34,   36,   37
  1,  6, 10, 11,   36,   41,   45,   46,   71,   76,   80,   81
  1,  8, 14, 15,   78,   85,   91,   92,  155,  162,  168,  169
  1, 12, 22, 23,  144,  155,  165,  166,  287,  298,  308,  309
  1, 14, 26, 27,  222,  235,  247,  248,  443,  456,  468,  469
  1, 18, 34, 35,  324,  341,  357,  358,  647,  664,  680,  681
  1, 20, 38, 39,  438,  457,  475,  476,  875,  894,  912,  913
  1, 24, 46, 47,  668,  691,  713,  714, 1335, 1358, 1380, 1381
  1, 30, 58, 59,  900,  929,  957,  958, 1799, 1828, 1856, 1857
  1, 32, 62, 63, 1148, 1179, 1209, 1210, 2295, 2326, 2356, 2357
  1, 38, 74, 75, 1518, 1555, 1591, 1592, 3035, 3072, 3108, 3109

Transpose: A286625.
Cf. A002110, A276943.
Row 1: A276155.
Column 1: A000012, Column 2: A008864, Column 3: A100484, Column 4: A072055, Column 5: A023523 (from its second term onward), Column 6: A286624 (= 1 + A123134), Column 11: 2*A123134, Column 13: 3*A006094.
Cf. A276616 (analogous array).

(define (A286623 n) (A286623bi (A002260 n) (A004736 n)))
(define (A286623bi row col) (/ (A276943bi row col) (A002110 (- row 1))))

A(n,k) = A276943(n, k) / A002110(n-1).

A286624 a(n) = (prime(1+n)*prime(n)) + prime(n) + 1.

Original entry on oeis.org

9, 19, 41, 85, 155, 235, 341, 457, 691, 929, 1179, 1555, 1805, 2065, 2539, 3181, 3659, 4149, 4825, 5255, 5841, 6637, 7471, 8723, 9895, 10505, 11125, 11771, 12427, 14465, 16765, 18079, 19181, 20851, 22649, 23859, 25749, 27385, 29059, 31141, 32579, 34753, 37055, 38215, 39401, 42189, 47265, 50845, 52211

Offset: 1

Antti Karttunen, Jun 28 2017

nonn

9 is the only perfect square in this sequence. - Altug Alkan, Jul 01 2017

Antti Karttunen, Table of n, a(n) for n = 1..10000

Row 6 of A286625 (column 6 of A286623). Column 4 of A328464.
One more than A123134.
Cf. A000040, A023523, A180932 (primes in this sequence).

Array[(#1 #2) + #1 + 1 & @@ Prime[# + {0, 1}] &, 49] (* Michael De Vlieger, Mar 14 2021 *)

lista(nn) = forprime(p=2, nn, print1(p*(nextprime(p+1)+1)+1, ", ")); \\ Altug Alkan, Jul 01 2017

(define (A286624 n) (+ (* (A000040 (+ 1 n)) (A000040 n)) (A000040 n) 1))
(define (A286624 n) (+ 1 (* (+ 1 (A000040 (+ 1 n))) (A000040 n))))

a(n) = (A000040(1+n)*A000040(n)) + A000040(n) + 1.
a(n) = 1 + A123134(n).
a(n) = A000040(n) + A023523(1+n).

A345727 a(n) = (prime(n)+1) * prime(n+1).

Original entry on oeis.org

9, 20, 42, 88, 156, 238, 342, 460, 696, 930, 1184, 1558, 1806, 2068, 2544, 3186, 3660, 4154, 4828, 5256, 5846, 6640, 7476, 8730, 9898, 10506, 11128, 11772, 12430, 14478, 16768, 18084, 19182, 20860, 22650, 23864, 25754, 27388, 29064, 31146, 32580, 34762

Offset: 1

Simon Strandgaard, Jul 20 2021

nonn

			a(1) = (prime(1)+1) * prime(2) = 3 *  3 =  9,
a(2) = (prime(2)+1) * prime(3) = 4 *  5 = 20,
a(3) = (prime(3)+1) * prime(4) = 6 *  7 = 42,
a(4) = (prime(4)+1) * prime(5) = 8 * 11 = 88.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A006094, A008864, A123134, A180617.

A345727 := proc(n)
    (ithprime(n)+1)*ithprime(n+1) ;
end proc:
seq(A345727(n),n=1..10) ; # R. J. Mathar, Aug 16 2021

(Prime@#+1)Prime[#+1]&/@Range@50 (* Giorgos Kalogeropoulos, Jul 23 2021 *)
(#[[1]]+1)#[[2]]&/@Partition[Prime[Range[50]],2,1] (* Harvey P. Dale, Jan 08 2023 *)

for(n=1, 100, print1((prime(n)+1)*prime(n+1), ", "))

require 'prime'
values = []
primes = Prime.first(20)
primes.each_index do |n|
    next if n < 1
    values << (primes[n - 1] + 1) * primes[n]
end
p values

a(n) = A008864(n)*A000040(n+1).
a(n) = A180617(n)-A008864(n).
a(n) = A006094(n)+A000040(n+1).

A123139 a(n) = prime(n)*(prime(n + 1) + 1) - (n^3 + sum of digits of n^3).

Original entry on oeis.org

6, 2, 4, 10, 21, 9, -13, -64, -57, -73, -161, -192, -412, -697, -855, -935, -1272, -1702, -2063, -2754, -3439, -4031, -4714, -5120, -5750, -7098, -8586, -10201, -11989, -12545, -13055, -14716, -16784, -18473, -20253, -22825, -24924, -27514, -30288, -32870, -36369, -39363, -42481, -46996, -51743

Offset: 1

Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 30 2006

A. Frank & P. Jacqueroux, International Contest, 2001. Item 30 = Item 21 - Item 24.

Table[Prime[n](Prime[n+1]+1)-(n^3+Total[IntegerDigits[n^3]]),{n,50}] (* Harvey P. Dale, Jul 03 2021 *)

for(n=1,50,sda=eval(Vec(Str(n^3)));print1(prime(n)*(prime(n+1)+1)-(n^3+sum(i=1,length(sda),sda[i])),","))

a(n) = A123134(n) - A123135(n). - Michel Marcus, Dec 03 2013

cp's OEIS Frontend

A286623 Square array A(n,k) = A276943(n,k)/A002110(n-1), read by descending antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Scheme

Formula

A286624 a(n) = (prime(1+n)*prime(n)) + prime(n) + 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Scheme

Formula

A345727 a(n) = (prime(n)+1) * prime(n+1).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Ruby

Formula

A123139 a(n) = prime(n)*(prime(n + 1) + 1) - (n^3 + sum of digits of n^3).

Views

Author

Keywords

Links

Programs

Mathematica

PARI

Formula