A335593 -id:A335593

Search: a335593 -id:a335593

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A336738

Primes abs(A335592(k))/2 for k in A335593.

+20
4

1399, 17939, 32869, 149759, 282349, 458929, 388099, 615389, 634169, 585619, 926179, 1053449, 1876339, 1336529, 2056829, 2156369, 2695249, 2653699, 2819779, 2501449, 1461709, 2176679, 3457969, 2549479, 3433819, 5299219, 4845499, 4774619, 7874749, 8796049, 9139469, 9029399, 7075759, 5156299

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

All terms end in 9 (or 1, if there are any with A335592(k) < 0).

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = abs(A335592(A335593(n)))/2.

EXAMPLE

A335593(3) = 27, A335592(27) = det(631, 563; 577, 619) = 65738 = 2*32869

so a(3) = 32869.

MAPLE

count:= 0: R:= NULL:

L:= [-9, -7, -3, -1]:

for k from 1 while count < 100 do

for i from 1 to 4 do

for x from L[i]+10 by 10 do until isprime(x);

L[i]:= x;

od;

v:= L[1]*L[4]-L[2]*L[3];

if isprime(abs(v)/2) then count:= count+1; R:= R, abs(v)/2; fi

od:

CROSSREFS

Cf. A335592, A335593.

KEYWORD

nonn,base,look

AUTHOR

J. M. Bergot and Robert Israel, Jan 27 2021

STATUS

approved

A335592

a(n) is the determinant of the 2 X 2 matrix whose entries (when read by rows) are the n-th primes ending in 1, 3, 7, 9 respectively.

+10
4

188, 678, 1568, 2798, 2768, 3928, 9328, 9418, 16918, 12418, 19428, 19578, 16898, 34698, 28028, 30988, 35878, 58528, 53908, 52318, 54938, 37308, 53098, 49888, 49758, 68688, 65738, 74328, 96558, 100098, 95548, 121898, 119108, 117438, 104078, 140698, 156588, 143168, 222888, 226608, 196448, 160448

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

All terms == 8 (mod 10).

Are there negative terms? The first 10^7 are positive.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

The first primes ending in 1,3,7,9 are 11,3,7,19, so a(1) = 11*19 - 3*7 = 188.

The second primes ending in 1,3,7,9 are 31,13,17,29, so a(2) = 31*29 - 13*17 = 678.

The third primes ending in 1,3,7,9 are 41,23,37,59, so a(3) = 41*59 - 23*37 = 1568.

MAPLE

R:= NULL:

L:= [-9, -7, -3, -1]:

for k from 1 to 100 do

for i from 1 to 4 do

for x from L[i]+10 by 10 do until isprime(x);

L[i]:= x;

od;

R:= R, L[1]*L[4]-L[2]*L[3];

od:

CROSSREFS

Cf. A335581, A335593, A336738.

KEYWORD

nonn,base,look

AUTHOR

J. M. Bergot and Robert Israel, Jan 27 2021

STATUS

approved

A337146

Numbers k such that abs(A337145(k))/8 is prime.

+10
3

1, 13, 41, 50, 53, 62, 67, 76, 89, 98, 108, 113, 137, 180, 211, 225, 236, 240, 250, 281, 293, 300, 303, 308, 355, 362, 384, 392, 393, 400, 414, 425, 434, 458, 468, 477, 489, 525, 588, 589, 593, 625, 653, 662, 664, 671, 673, 674, 696, 698, 732, 758, 765, 795, 800, 819, 831, 851, 880, 916, 933, 938

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(3) = 41 is a term because A337145(41) = det(1097, 883; 877, 967) = 286408 = 8*35801 and 35801 is prime.

MAPLE

R:= NULL:

count:= 0:

L:= [-7, -5, -3, -1]:

for k from 1 while count < 100 do

for i from 1 to 4 do

for x from L[i]+8 by 8 do until isprime(x);

L[i]:= x;

od;

v:= abs(L[1]*L[4]-L[2]*L[3])/8;

if isprime(v) then count:= count+1; R:= R, k; fi

od:

CROSSREFS

Cf. A335593, A337145, A337147.

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Jan 27 2021

STATUS

approved

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