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.

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A047981 a(n) = A047980(2n).

Original entry on oeis.org

3, 7, 17, 71, 19, 59, 167, 757, 197, 159, 799, 227, 317, 415, 361, 521, 3289, 2633, 1637, 1861, 1691, 1997, 2053, 4097, 6437, 5731, 9199, 11603, 5641, 3833, 26885, 6637, 26815, 32117, 18637, 29933, 31667, 5227, 19891, 47303, 54973, 5207, 59537
Offset: 1

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Examples

			First example: a(1)=3 since in 3k+1 sequence, the first term is 3, a prime and the d=2 is the smallest such difference. The next such progression is 5k+1 because 5*2+1=11 is prime. 2nd example: here at n=6 a(6)=59. This means that 2n=12 occurs first in A034693 at its position 59, which means that its first prime is 12*59+1=709. arises as 12th term (such progressions are: 59k+1,85k+1,133k+1, etc.)
		

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Formula

a(n) = min {k}: A034693(a(n)) is an even number such that in a(n)*k+1 progression the first prime occurs at even 2n=k position.

A047982 a(n) = A047980(2n+1).

Original entry on oeis.org

1, 24, 38, 184, 368, 668, 634, 512, 1028, 1468, 3382, 4106, 10012, 7628, 11282, 38032, 53630, 37274, 63334, 34108, 102296, 119074, 109474, 117206, 60664, 410942, 204614, 127942, 125618, 595358, 517882, 304702, 352022, 1549498, 651034, 506732, 5573116, 1379216, 1763144
Offset: 0

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Examples

			a(2)=38 because A034693(38) = 2*2+1 = 5 is the first 5; 5*38+1 = 191 is the first prime. The successive progressions in which the first prime appears at position 5 are as follows: 38k+1, 62k+1, 164k+1. 2nd example: a(20)=102296 because. The first 41 appears in A034693 at this index. Also 102296*(2*20+1)+1 = 102296*41+1 = 4194137 is the first prime in {102296k+1}. The next progression with this position of prime emergence is 109946k+1 (the corresponding prime is 4507787).
		

Crossrefs

Formula

a(n) = min {d}: A034693(a(n)) is an odd number k such that in a(n)*k+1 progression the first prime occurs at k=2n+1 position.

Extensions

More terms from Michel Marcus, Sep 01 2019
Showing 1-2 of 2 results.