A182178 Beginning with 1, smallest positive integer not yet in the sequence such that two adjacent digits of the sequence (also ignoring commas between terms) sum to a prime.

1, 2, 3, 4, 7, 6, 5, 8, 9, 20, 21, 11, 12, 14, 16, 50, 23, 25, 29, 41, 43, 47, 49, 83, 85, 61, 65, 67, 411, 111, 112, 30, 32, 34, 38, 52, 56, 58, 92, 94, 70, 74, 76, 114, 98, 302, 116, 120, 202, 121, 123, 89, 203, 205, 207, 412, 125, 211, 129, 212, 141, 143

Offset

1,2

Comments

See A219110 for the numbers which do not occur in this sequence. See A219250 for the analog when "sum" is replaced with "absolute difference", and A219248-A219251 for related sequences. - M. F. Hasler, Apr 11 2013

Links

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

Example

20 follows 9 since 9+2 and 2+0 is prime, and no number less than 20 (not already in the sequence) satisfies the stated property.

Mathematica

a[1] = 1; a[n_] := a[n] = For[id = IntegerDigits[a[n-1]]; k = 1, True, k++, If[FreeQ[Array[a, n-1], k], dd = Join[id, IntegerDigits[k]]; If[And @@ PrimeQ /@ Plus @@@ Transpose[{Most[dd], Rest[dd]}], Return[k]]]]; Array[a, 62] (* Jean-François Alcover, Apr 17 2013 *)

Prog

(PARI) A182178_vec={(n, a=[1], u=0)->while(#a<n, u+=1<<a[#a]; for(t=a[1]+1, 9e9, bittest(u, t)&next; my(d=concat(a[#a]%10, digits(t))); for(i=2, #d, isprime(d[i-1]+d[i])||next(2)); a=concat(a, t); break)); a} \\ M. F. Hasler, Apr 11 2013

Crossrefs

Cf. A182175, A182177.

Sequence in context: A332212 A085161 A085162 * A326316 A361444 A305417

Adjacent sequences: A182175 A182176 A182177 * A182179 A182180 A182181

Keyword

nonn,base,easy

Author

Jim Nastos and Eric Angelini, Apr 16 2012

Status

approved