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

1,3

Comments

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

Links

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

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[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]}]], 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[i-1]+n[i])||return) \\ M. F. Hasler, Oct 27 2014

Crossrefs

These are the candidate numbers for extending A182178.

Cf. A219110.

Sequence in context: A178843 A252996 A252495 * A254329 A128870 A355620

Adjacent sequences: A182172 A182173 A182174 * A182176 A182177 A182178

Keyword

nonn,base

Author

Jim Nastos, Apr 16 2012

Status

approved