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A103608 Prime centuries with exactly one prime year in each decade. 2
3677, 16447, 118463, 357131, 368153, 582017, 932413, 1239443, 2284027, 2421473, 3900931, 4943777, 6850463, 6966059, 10448783, 11548777, 12849937, 15198811, 16031237, 17315087, 19443679, 20075687, 20614667, 20850223, 21392099, 22586903, 22634153, 23013773, 24753761 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Or: Primes p such that there is exactly one prime in each decade [10d-9, 10d] for 10p-9 <= d < 10p. - M. F. Hasler, May 02 2019
LINKS
EXAMPLE
4073 is not in the sequence because 407203 and 407207 are both prime and in the same decade. 211217 is not in the sequence because 21121691 and 21121697 are both prime and in the same decade. 5046053 is not in the sequence because 504605291 and 504605293 are both prime and in the same decade. - R. J. Mathar, May 02 2019
MAPLE
isA103608 := proc(n)
local p, dec ;
if not isprime(n) then
false;
else
p := 100*(n-1) ;
for dec from 0 to 9 do
p := nextprime(p) ;
if modp(floor(p/10), 10) <> dec then
return false;
end if;
end do:
p := nextprime(p) ;
if p > 100*n then
true ;
else
false;
end if;
end if;
end proc:
for i from 1 do
p := ithprime(i) ;
if isA103608(p) then
printf("%d, \n", p) ;
end if;
end do: # R. J. Mathar, May 02 2019
PROG
(PARI) select( is_A103608(p)={for(k=10*p-9, 10*p, #primes([10*k-9, 10*k])==1||return); isprime(p)}, primes(10^5)) \\ M. F. Hasler, May 02 2019
CROSSREFS
Cf. A156115, A307890 (allowing more than one prime in first and last decade).
Sequence in context: A216139 A250702 A307890 * A204757 A250875 A252311
KEYWORD
nonn,less
AUTHOR
R. J. Mathar, _M. Hasler_, May 02 2019
STATUS
approved

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Last modified June 21 13:19 EDT 2024. Contains 373544 sequences. (Running on oeis4.)