|
Search: id:A057620
|
|
|
| A057620 |
|
Initial prime in first sequence of n primes congruent to 1 modulo 6. |
|
+0
4
|
|
| 7, 31, 151, 1741, 1741, 1741, 19471, 118801, 148531, 148531, 406951, 2339041, 2339041, 51662593, 51662593, 73451737, 232301497, 450988159, 1444257673, 1444257673, 1444257673, 24061965043, 24061965043, 43553959717, 43553959717
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
REFERENCES
|
R. K. Guy, "Unsolved Problems in Number Theory", A4
|
|
LINKS
|
J. K. Andersen, Consecutive Congruent Primes.
|
|
EXAMPLE
|
a(6) = 1741 because this number is the first in a sequence of 6 consecutive primes all of the form 3n + 1.
|
|
MATHEMATICA
|
NextPrime[ n_Integer ] := Module[ {k = n + 1}, While[ ! PrimeQ[ k ], k++ ]; Return[ k ]]; PrevPrime[ n_Integer ] := Module[ {k = n - 1}, While[ ! PrimeQ[ k ], k-- ]; Return[ k ]]; p = 0; Do[ a = Table[ -1, {n} ]; k = Max[ 1, p ]; While[ Union[ a ] != {1}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 3 ]], -n ]]; p = NestList[ PrevPrime, k, n ]; Print[ p[[ -2 ] ]]; p = p[[ -1 ]], {n, 1, 18} ]
|
|
CROSSREFS
|
Cf. A057619, A057622, A057624.
Sequence in context: A086901 A003526 A121517 this_sequence A055625 A102239 A139151
Adjacent sequences: A057617 A057618 A057619 this_sequence A057621 A057622 A057623
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 09 2000
|
|
EXTENSIONS
|
More terms from Don Reble (djr(AT)nk.ca), Nov 16 2003
More terms from Jens Kruse Andersen (jens.k.a(AT)get2net.dk), May 30 2006
|
|
|
Search completed in 0.002 seconds
|
