A182175 Numbers with the property that every pair of adjacent digits sum to a prime number.

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

Offset: 1

Author

Jim Nastos, Apr 16 2012

Keywords

• nonn
• base

Comments

Complement of A219110. - M. F. Hasler, Apr 11 2013

Examples

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

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

These are the candidate numbers for extending A182178.

Cf. A219110.

Programs

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[j-1]) od:
`union`({0},seq(S[j],j=1..N));
# if using Maple 11 or lower, uncomment the next line:
# sort(convert(%,list));
# Robert Israel, Oct 27 2014

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]}]] (* T. D. Noe, Aug 21 2012 and Apr 17 2013; modified by Zak Seidov, Oct 28 2014 *)

PARI

is_A182175(n)=!for(i=2, #n=digits(n), isprime(n[i-1]+n[i])||return) \\ M. F. Hasler, Oct 27 2014