A249012 Smallest prime such that the multisets of the next n and the following n prime gaps are equal.

3, 5, 3, 23, 11, 13, 23, 263, 304349, 5644939, 151, 5644927, 18068879

Offset

1,1

Comments

Smallest prime(k) such that the multiset of the n prime gaps after prime(k) equals the multiset of the n prime gaps after prime(n+k).

Links

Table of n, a(n) for n=1..13.

Abhiram R Devesh, Python Code for generating this sequence

Example

a(4)=23 as the prime gaps {2, 4, 6, 6} get repeated for (23, 29, 31, 37, 41) and (41, 43, 47, 53, 59).
a(6)=13 as the prime gaps {4, 2, 4, 6, 6, 2} get repeated for (13, 17, 19, 23, 29, 31, 37) and (37, 41, 43, 47, 53, 59, 61).

Maple

A249012 := proc(n)
    local j, gapsetp, gapsetq;
    for j from 1 do
        gapsetp := [seq(ithprime(j+i)-ithprime(j+i-1), i=1..n)]  ;
        gapsetq := [seq(ithprime(j+n+i)-ithprime(j+n+i-1), i=1..n)]  ;
        if sort(gapsetp) = sort(gapsetq) then
            return ithprime(j) ;
        end if;
    end do:
end proc:
for n from 1 do
    print(A249012(n)) ;
end do: # R. J. Mathar, Nov 17 2014

Prog

(PARI) test(p, n)=my(v=vector(n, i, -p+(p=nextprime(p+1))), u=vector(n, i, -p+(p=nextprime(p+1)))); vecsort(u)==vecsort(v)
a(n)=forprime(p=3, , if(test(p, n), return(p))) \\ Charles R Greathouse IV, Oct 21 2014

Crossrefs

Cf. A249011 (similar but with exactly the same prime gaps).

Sequence in context: A094466 A134771 A080349 * A249908 A195418 A366857

Adjacent sequences: A249009 A249010 A249011 * A249013 A249014 A249015

Keyword

nonn,more

Author

Abhiram R Devesh, Oct 18 2014

Status

approved