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

1,1

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

Table of n, a(n) for n=1..29.

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

Adjacent sequences: A103605 A103606 A103607 * A103609 A103610 A103611

Keyword

nonn,less

Author

R. J. Mathar, _M. Hasler_, May 02 2019

Status

approved