Yagel Numbers in the OEIS

The grid gives both a square array and sequences of prime locations. Each sequence below has its own definition, data and verification programs.

A400659 · First primes by row

Published in the OEIS. The least exponent at which each row of the minus face reaches a prime. The first 100 terms have standalone primality and minimality proofs.

Term table and proofs →

A401136 · The minus-face array

Published in the OEIS. The whole minus face, read by antidiagonals, starting 1; 3, 5; 7, 17, 29; 15, 53, 149, 209; …

Definition, b-file and programs →

The OEIS uses $n$ as the sequence index; each sequence page explains how its notation corresponds to the paper's order $k$ and exponent $n$ .

The grid's edges in the OEIS

The first row and the first column of the grid, on both faces, were in the OEIS before this project, as were rows 2 and 3. Each sequence below is written in this site's letters; the OEIS entries use their own.

edge of the grid	numbers	OEIS
row $k = 1$ , minus face	Mersenne numbers $2^n - 1$ : exponents giving primes	A000043
row $k = 2$ , both faces	$2\cdot 3^n - 1$ and $2\cdot 3^n + 1$ : exponents giving primes	A003307, A003306
row $k = 3$ , both faces	$6\cdot 5^n - 1$ and $6\cdot 5^n + 1$ : exponents giving primes	A257790, A143279
column $n = 1$ , minus face	numbers $p_k\# - 1$ : the orders $k$ , and the primes $p_k$ , at which it is prime	A057704, A006794
column $n = 1$ , plus face	Euclid numbers $p_k\# + 1$ : the orders $k$ , and the primes $p_k$ , at which it is prime	A014545, A005234
the coefficients	primorials $p_k\#$ , and the primes	A002110, A000040

Checked 9 October 2026: on every edge listed, the OEIS terms agree with this site's catalogue of proven primes as far as both reach.