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A293393
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Initial member of 10 consecutive primes {a, b, c, d, e, f, g, h, i, j} such that (j - e) = (i - d) = (h - c) = (g - b) = (f - a).
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2
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541, 547, 557, 1019, 4229, 4231, 35099, 59617, 91199, 105997, 708251, 998969, 1208209, 1260323, 1376461, 1435997, 1556393, 1752197, 1996217, 2092249, 2152811, 2271383, 2349917, 3011011, 3919199, 3919211, 4020167, 4020197, 4089037, 4089073, 4797503, 4897331, 5124023
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OFFSET
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1,1
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COMMENTS
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12689273 is the smallest term such that 12689273 +- 6 are both prime.
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LINKS
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EXAMPLE
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541 is a term because it is the initial member of 10 consecutive primes {541, 547, 557, 563, 569, 571, 577, 587, 593, 599} = {a, b, c, d, e, f, g, h, i, j}: {(j - e) = (i - d) = (h - c) = (g - b) = (f - a)} = {(599 - 569) = (593 - 563) = (587 - 557) = (577 - 547) = (571 - 541)} = 30.
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MAPLE
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A293393:= proc(n)local a, b, c, d, e, f, g, h, i, j; a:=ithprime(n); b:=ithprime(n+1); c:=ithprime(n+2); d:=ithprime(n+3); e:=ithprime(n+4); f:=ithprime(n+5); g:=ithprime(n+6); h:=ithprime(n+7); i:=ithprime(n+8); j:=ithprime(n+9); if (j - e) = (i - d) and (j - e)= (h - c) and (j - e)= (g - b) and (j - e)= (f - a)then RETURN (a); fi; end: seq(A293393(n), n=1..500000);
# Alternative:
P:= select(isprime, [seq(i, i=3..10^7, 2)]):
Q:= P[6..-1]-P[1..-6]:
J:= select(t -> nops(convert(Q[t..t+4], set))=1, [$1..nops(Q)-4]):
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MATHEMATICA
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Select[Partition[Prime@ Range[10^6], 10, 1], Equal[#10 - #5, #9 - #4, #8 - #3, #7 - #2, #6 - #1] & @@ # &][[All, 1]] (* Michael De Vlieger, Oct 08 2017 *)
udQ[n_]:=Length[Union[Differences[TakeDrop[n, 5]][[1]]]]==1; Select[ Partition[ Prime[ Range[360000]], 10, 1], udQ][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 19 2018 *)
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PROG
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(PARI) for(n = 1, 50000, a = prime(n); b = prime(n+1); c = prime(n+2); d = prime(n+3); e = prime(n+4); f = prime(n+5); g = prime(n+6); h = prime(n+7); i = prime(n+8); j = prime(n+9); if((j - e)==(i - d) && (j - e)==(h - c) && (j - e)==(g - b) && (j - e)==(f - a), print1 (a, " , ")));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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