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 A031924 Primes followed by a gap of 6, i.e., next prime is p + 6. 52
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 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 EXAMPLE 23 is a term as the next prime 29 = 23 + 6. 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], 2, 1], Last[#] - First[#] == 6 &]][] (* Bruno Berselli, Apr 09 2013 *) PROG (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 (MAGMA) [p: p in PrimesUpTo(1200) | NextPrime(p)-p eq 6]; // Bruno Berselli, Apr 09 2013 (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 CROSSREFS Cf. A001359, A023201, A031925; A031924 and A007529 together give A023201. Sequence in context: A124582 A130796 A258578 * A257528 A240886 A162587 Adjacent sequences:  A031921 A031922 A031923 * A031925 A031926 A031927 KEYWORD nonn AUTHOR EXTENSIONS New name from M. F. Hasler, Jan 02 2020 STATUS approved

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Last modified June 24 05:46 EDT 2021. Contains 345416 sequences. (Running on oeis4.)