A031924 Primes followed by a gap of 6, i.e., next prime is p + 6.

23, 31, 47, 53, 61, 73, 83, 131, 151, 157, 167, 173, 233, 251, 257, 263, 271, 331, 353, 367, 373, 383, 433, 443, 503, 541, 557, 563, 571, 587, 593, 601, 607, 647, 653, 677, 727, 733, 751, 941, 947, 971, 977, 991, 1013, 1033, 1063, 1097, 1103, 1117, 1123, 1181

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Comments

Original name: Lower prime of a difference of 6 between consecutive primes.

Conjecture: The sequence is infinite and for every n >= 7746, a(n+1) < a(n)^(1+1/n). Namely for n >= 7746, a(n)^(1/n) is a strictly decreasing function of n (See comment lines of the sequence A248855). - Jahangeer Kholdi and Farideh Firoozbakht, Nov 29 2014

Examples

			23 is a term as the next prime 29 = 23 + 6.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• OEIS wiki, Consecutive primes in arithmetic progression: CPAP with given gap, updated Jan. 2020
• Index entries for primes, gaps between

Crossrefs

Cf. A001359, A023201, A031925; A031924 and A007529 together give A023201.

Programs

GAP

P:=Filtered([1..1200],IsPrime);;
List(Filtered([1..Length(P)-1],i->P[i+1]-P[i]=6),k->P[k]); # Muniru A Asiru, Jan 30 2019

Magma

[p: p in PrimesUpTo(1200) | NextPrime(p)-p eq 6]; // Bruno Berselli, Apr 09 2013

Maple

A031924 := proc(n)
    option remember;
    if n = 1 then
        return 23;
    else
        p := nextprime(procname(n-1)) ;
        q := nextprime(p) ;
        while q-p <> 6 do
            p := q ;
            q := nextprime(p) ;
        end do:
        return p;
    end if;
end proc: # R. J. Mathar, Jan 23 2013

Mathematica

Transpose[Select[Partition[Prime[Range[200]], 2, 1], Last[#] - First[#] == 6 &]][[1]] (* Bruno Berselli, Apr 09 2013 *)

PARI

is(n)=isprime(n)&&nextprime(n+1)-n==6 \\ Charles R Greathouse IV, Mar 21 2013

PARI

apply( A031924(n,p=2,show=0,g=6)={forprime(q=p+1,, p+g!=(p=q) || (show&&print1(p-g",")) || n-- || return(p-g))}, [1..99]) \\ Use nxt(p)=A031924(1,p) to get the term following p, use show=1 to print all a(1..n), g to select a different gap. - M. F. Hasler, Jan 02 2020

Extensions

New name from M. F. Hasler, Jan 02 2020