

A182175


Numbers with the property that every pair of adjacent digits sum to a prime number.


12



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

1,3


COMMENTS



LINKS



EXAMPLE

983 is in the sequence since 9+8 is prime and 8+3 is prime.


MAPLE

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[j1]) od:
`union`({0}, seq(S[j], j=1..N));
# if using Maple 11 or lower, uncomment the next line:
# sort(convert(%, list));


MATHEMATICA

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 *)


PROG

(PARI) is_A182175(n)=!for(i=2, #n=digits(n), isprime(n[i1]+n[i])return) \\ M. F. Hasler, Oct 27 2014


CROSSREFS

These are the candidate numbers for extending A182178.


KEYWORD

nonn,base


AUTHOR



STATUS

approved



