A128472 -id:A128472 - cp's OEIS frontend

A155897 Square matrix T(m,n)=1 if (2m+1)^n-2 is prime, 0 otherwise; read by antidiagonals.

0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset: 1

M. F. Hasler, Feb 01 2009

In some sense a "minimal" possible generalization of the pattern of Mersenne primes (cf. A000043) is to consider powers of odd numbers (> 1) minus 2. Since even powers obviously correspond to an odd power of the base squared, it is sufficient to consider only odd powers, cf. A155899.

Cf. A084714, A128472, A094786, A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.

T = matrix( 19,19,m,n, isprime((2*m+1)^n-2)) ;
A155897 = concat( vector( vecmin( matsize(T)), i, vector( i, j, T[j,i-j+1])))

A155898 Square matrix T(m,n)=1 if (2m+1)^(2n)-2 is prime, 0 otherwise; read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1

Offset: 1

M. F. Hasler, Feb 01 2009

In some sense the "minimal" possible generalization of the pattern of Mersenne primes (cf. A000043) is to consider powers of odd numbers minus 2. Here only even powers are considered (which obviously correspond to an odd power of the base squared).

Cf. A084714, A128472, A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.

T = matrix( 19,19,m,n, isprime((2*m+1)^(2*n)-2)) ;
A155898 = concat( vector( vecmin( matsize(T)), i, vector( i, j, T[j,i-j+1])))

A204578 Primes of the form 5^k-2.

Original entry on oeis.org

3, 23, 6103515623, 1490116119384765623, 88817841970012523233890533447265623, 11754943508222875079687365372222456778186655567720875215087517062784172594547271728515623, 44841550858394146269559346665277316200968382140048504696226185084473314645947539247572422027587890623

Offset: 1

M. F. Hasler, Jan 30 2012

See the sequence A109080 for the corresponding exponents k.

The number a(3) = 6103515623 is also in A095304, A104090 and A128472.

Cf. A109080.

for(i=0,999, ispseudoprime(t=5^i-2) & print1(t","))

a(n) = 5^A109080(n)-2.

cp's OEIS Frontend

A155897 Square matrix T(m,n)=1 if (2m+1)^n-2 is prime, 0 otherwise; read by antidiagonals.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A155898 Square matrix T(m,n)=1 if (2m+1)^(2n)-2 is prime, 0 otherwise; read by antidiagonals.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

A204578 Primes of the form 5^k-2.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

Formula