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A182175
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Numbers with the property that every pair of adjacent digits sum to a prime number.
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12
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 16, 20, 21, 23, 25, 29, 30, 32, 34, 38, 41, 43, 47, 49, 50, 52, 56, 58, 61, 65, 67, 70, 74, 76, 83, 85, 89, 92, 94, 98, 111, 112, 114, 116, 120, 121, 123, 125, 129, 141, 143, 147, 149, 161, 165, 167, 202, 203, 205, 207, 211, 212, 214, 216, 230, 232, 234
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OFFSET
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1,3
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COMMENTS
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LINKS
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EXAMPLE
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983 is in the sequence since 9+8 is prime and 8+3 is prime.
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MAPLE
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N:= 4: # to get all terms with up to N digits.
for p from 0 to 9 do P[p]:= select(t -> isprime(t+p), [$0..9]) od:
F:= proc(t) local r, p; r:= t mod 10; op(map(`+`, P[r], 10*t)) end proc:
S[1]:= {$1..9}:
for j from 2 to N do S[j]:= map(F, S[j-1]) od:
`union`({0}, seq(S[j], j=1..N));
# if using Maple 11 or lower, uncomment the next line:
# sort(convert(%, list));
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MATHEMATICA
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fQ[n_] := Module[{d = IntegerDigits[n], s}, s = Most[d] + Rest[d]; And @@ PrimeQ[s]]; Flatten[Join[{Range[0, 9], Select[Range[11, 300], fQ]}]], fQ] (* T. D. Noe, Aug 21 2012 and Apr 17 2013; modified by Zak Seidov, Oct 28 2014 *)
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PROG
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(PARI) is_A182175(n)=!for(i=2, #n=digits(n), isprime(n[i-1]+n[i])||return) \\ M. F. Hasler, Oct 27 2014
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CROSSREFS
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These are the candidate numbers for extending A182178.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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