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A215420
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Primes that remain prime when a single digit 7 is inserted between any two consecutive digits or as the leading or trailing digit.
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12
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3, 19, 97, 433, 487, 541, 691, 757, 853, 1471, 2617, 2953, 4507, 6481, 7351, 7417, 8317, 13177, 31957, 42457, 46477, 47977, 50077, 59053, 71917, 73897, 74377, 77479, 77743, 77761, 79039, 99103, 175687, 220897, 271177, 360973
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..63 (* All terms up to and including the 1 millionth prime *)
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EXAMPLE
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59053 is prime and also 590537, 590573,590753, 597053, 579053, 759053.
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MAPLE
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A215420:=proc(q, x)
local a, b, c, d, i, n, ok;
for n from 1 to q do
a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od;
a:=ithprime(n); ok:=1;
for i from 0 to b do
c:=a+9*10^i*trunc(a/10^i)+10^i*x; if not isprime(c) then ok:=0; break; fi;
od;
if ok=1 then print(ithprime(n)); fi;
od; end:
A215420(1000, 7);
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MATHEMATICA
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Select[Prime[Range[31000]], AllTrue[FromDigits/@Table[Insert[ IntegerDigits[ #], 7, n], {n, IntegerLength[#]+1}], PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 29 2020 *)
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CROSSREFS
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Cf. A215417-A215419, A215421
Sequence in context: A049153 A074361 A126187 * A303542 A294251 A294392
Adjacent sequences: A215417 A215418 A215419 * A215421 A215422 A215423
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KEYWORD
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nonn,base
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AUTHOR
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Paolo P. Lava, Aug 10 2012
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STATUS
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approved
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