A103608 Prime centuries with exactly one prime year in each decade.
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
Offset: 1
Examples
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
Programs
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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
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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
Comments