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A031924
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Primes followed by a gap of 6, i.e., next prime is p + 6.
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57
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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23 is a term as the next prime 29 = 23 + 6.
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MAPLE
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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;
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MATHEMATICA
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Transpose[Select[Partition[Prime[Range[200]], 2, 1], Last[#] - First[#] == 6 &]][[1]] (* Bruno Berselli, Apr 09 2013 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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