A307890 Prime centuries with at least one prime year in each decade and exactly one prime year in decades 1 to 8.

3677, 4073, 16447, 118463, 211217, 357131, 368153, 582017, 932413, 1172777, 1239443, 2284027, 2421473, 3900931, 4943777, 5046053, 6850463, 6966059, 8046347, 10448783, 11548777, 12849937, 15198811, 16031237, 17315087, 19443679, 20075687, 20434811, 20462861, 20614667

Offset

1,1

Comments

In other words, prime numbers p such that there are ten consecutive primes between p*100-100 and p*100, each of them in a different decade. (The P-div-10s are all different.) - Don Reble (djr(AT)nk.ca) May 02 2019

Links

Table of n, a(n) for n=1..30.

Example

4073 is in the sequence, representing the prime sequence 407203, 407207, 407219, 407221, 407233, 407249, 407257, 407263, 407273, 407287, 407291, 407299, with 2 primes in decades 0 and 9, and 1 prime in decades 1 to 8. - R. J. Mathar, May 03 2019

Maple

isA307890 := proc(n)
    local p, dec ;
    if not isprime(n) then
        false;
    else
        p := 100*(n-1) ;
        p := prevprime(p+10) ;
        for dec from 0 to 9 do
            if modp(floor(p/10), 10) <> dec then
                return false;
            end if;
            p := nextprime(p) ;
        end do:
        true ;
    end if;
end proc:
for i from 1 do
    p := ithprime(i) ;
    if isA307890(p) then
        printf("%d, \n", p) ;
    end if;
end do: # R. J. Mathar, May 03 2019

Crossrefs

Cf. A156115, super set of the primes in A103608.

Sequence in context: A250895 A216139 A250702 * A103608 A204757 A250875

Adjacent sequences: A307887 A307888 A307889 * A307891 A307892 A307893

Keyword

nonn,less

Author

Zak Seidov, Feb 27 2009

Status

approved