A138139 -id:A138139 - cp's OEIS frontend

A138140 Concatenation of terms of n-th row of the triangle of primes A138139.

2, 22, 232, 2332, 23532, 235532, 2357532, 23577532, 2357117532, 235711117532, 23571113117532, 2357111313117532, 235711131713117532, 23571113171713117532, 2357111317191713117532, 235711131719191713117532

Offset: 1

Omar E. Pol, Mar 09 2008

The first 10 members are palindromes A002113.

			.
n ... a(n)
1 ... 2
2 ... 22
3 ... 232
4 ... 2332
5 ... 23532
6 ... 235532
7 ... 2357532
8 ... 23577532
9 ... 2357117532
10 .. 235711117532
11 .. 23571113117532

Cf. A000040, A089182, A138139.

A037126 Triangle T(n,k) = prime(k) for k = 1..n.

Original entry on oeis.org

2, 2, 3, 2, 3, 5, 2, 3, 5, 7, 2, 3, 5, 7, 11, 2, 3, 5, 7, 11, 13, 2, 3, 5, 7, 11, 13, 17, 2, 3, 5, 7, 11, 13, 17, 19, 2, 3, 5, 7, 11, 13, 17, 19, 23, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 2, 3, 5, 7, 11, 13, 17

Offset: 1

Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998

Or, triangle read by rows in which row n lists first n primes.

Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A. Sequence A037126 is reluctant sequence of the prime numbers A000040. - Boris Putievskiy, Dec 12 2012

			Triangle begins:
..... 2
.... 2,3
... 2,3,5
.. 2,3,5,7
. 2,3,5,7,11
...

Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened
Boris Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732 [math.CO], 2012.

Cf. A000040, A002260, A037126, A138139, A138140, A138143.

Cf. A007504 (row sums).

P:=Filtered([1..200],IsPrime);;
T:=Flat(List([1..13],n->List([1..n],k->P[k]))); # Muniru A Asiru, Mar 16 2019

a037126 n k = a037126_tabl !! (n-1) !! (k-1)
a037126_row n = a037126_tabl !! (n-1)
a037126_tabl = map (`take` a000040_list) [1..]
-- Reinhard Zumkeller, Oct 01 2012

T:=(n,k)->ithprime(k): seq(seq(T(n,k),k=1..n),n=1..13); # Muniru A Asiru, Mar 16 2019

Flatten[ Table[ Prime[ i], {n, 12}, {i, n}]] (* Robert G. Wilson v, Aug 18 2005 *)
Module[{nn=15,prs},prs=Prime[Range[nn]];Table[Take[prs,n],{n,nn}]]// Flatten (* Harvey P. Dale, May 02 2017 *)

As a linear array, the sequence is a(n) = A000040(m), where m = n-t(t+1)/2, t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 12 2012

A138117 Triangle read by rows: row n lists the first 2n-1 prime numbers.

Original entry on oeis.org

2, 2, 3, 5, 2, 3, 5, 7, 11, 2, 3, 5, 7, 11, 13, 17, 2, 3, 5, 7, 11, 13, 17, 19, 23, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Offset: 1

Omar E. Pol, Mar 14 2008, corrected Mar 15 2008

			Triangle begins:
....... 2
..... 2,3,5
... 2,3,5,7,11
. 2,3,5,7,11,13,17

Cf. A000040, A037126, A138139, A138143.

nn=10;Flatten[Table[Take[Prime[Range[2nn+1]],2n+1],{n,0,nn}]] (* Harvey P. Dale, Aug 16 2011 *)

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A138140 Concatenation of terms of n-th row of the triangle of primes A138139.

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A037126 Triangle T(n,k) = prime(k) for k = 1..n.

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A138117 Triangle read by rows: row n lists the first 2n-1 prime numbers.

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