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 A103608 Prime centuries with exactly one prime year in each decade. 2

%I #28 May 16 2019 04:54:33

%S 3677,16447,118463,357131,368153,582017,932413,1239443,2284027,

%T 2421473,3900931,4943777,6850463,6966059,10448783,11548777,12849937,

%U 15198811,16031237,17315087,19443679,20075687,20614667,20850223,21392099,22586903,22634153,23013773,24753761

%N Prime centuries with exactly one prime year in each decade.

%C 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

%e 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

%p isA103608 := proc(n)

%p local p,dec ;

%p if not isprime(n) then

%p false;

%p else

%p p := 100*(n-1) ;

%p for dec from 0 to 9 do

%p p := nextprime(p) ;

%p if modp(floor(p/10),10) <> dec then

%p return false;

%p end if;

%p end do:

%p p := nextprime(p) ;

%p if p > 100*n then

%p true ;

%p else

%p false;

%p end if;

%p end if;

%p end proc:

%p for i from 1 do

%p p := ithprime(i) ;

%p if isA103608(p) then

%p printf("%d,\n",p) ;

%p end if;

%p end do: # _R. J. Mathar_, May 02 2019

%o (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

%Y Cf. A156115, A307890 (allowing more than one prime in first and last decade).

%K nonn,less

%O 1,1

%A _R. J. Mathar_, _M. Hasler_, May 02 2019

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Last modified July 19 16:24 EDT 2024. Contains 374410 sequences. (Running on oeis4.)