A138140 -id:A138140 - cp's OEIS frontend

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

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

A089182 Prime digit palindromes 2,...,23577532 continued by adding 10^(n-k) and 10^(k-1) times prime(k).

Original entry on oeis.org

2, 22, 232, 2332, 23532, 235532, 2357532, 23577532, 235817532, 2358217532, 23582417532, 235824417532, 2358248417532, 23582488417532, 235824908417532, 2358249108417532, 23582491508417532, 235824915508417532

Offset: 1

Roger L. Bagula, Dec 07 2003

Original definition: Overlapping prime-based palindromic sequence.

Only the first 8 terms are truly palindromes: a modulo 10 version of this would work with a limited digit set {1,2,3,5,7,9} with 2 and 5 only occurring as 1st and 3rd digit to either side.

Cf. A007907, A138140.

a[m_]=Delete[Table[If [ Floor[m/2]-n>=0, Prime[ n], Prime[m-n]], {n, 1, m}], m] b=Table[Sum[a[m][[i]]*10^(i-1), {i, 1, m-1}], {m, 2, digits}]

a(n) = Sum_{k=1..floor(n/2)} prime(k)*(10^(n-k) + 10^(k-1)) + (n mod 2)*prime((n+1)/2)*10^floor(n/2). - M. F. Hasler, Apr 06 2009

Edited by M. F. Hasler, Apr 06 2009

cp's OEIS Frontend

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

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