A330434 a(1) = 1, a(2) = 2; thereafter a(n) = smallest number not occurring earlier such that the sum of three successive digits is prime.

1, 2, 4, 5, 8, 6, 3, 20, 9, 22, 7, 24, 10, 11, 13, 17, 31, 15, 51, 19, 35, 33, 53, 37, 39, 55, 71, 57, 73, 77, 91, 75, 59, 95, 93, 79, 110, 12, 21, 28, 14, 25, 42, 18, 23, 26, 32, 27, 40, 16, 41, 60, 50, 29, 62, 30, 43, 44, 34, 45, 48, 54, 49, 46, 38, 63, 80, 52, 47, 64, 36, 83, 68, 56, 61, 66, 58, 65, 84, 70, 67, 401

Offset

1,2

Links

Carole Dubois, Table of n, a(n) for n = 1..508

Example

After 8 and 6 the next term is 3 as 8+6+3 = 17 is a prime;
After 6 and 3 the next term is 20 as 6+3+2 = 11 and 3+2+0 = 5 are primes;
After 20 the next term is 9 as 2+0+9 = 11 is a prime; etc.

Mathematica

Nest[Append[#, Block[{k = 3}, While[Nand[FreeQ[#, k], AllTrue[Table[Total@ #[[i ;; i + 2]], {i, Length@ # - 2}], PrimeQ] &@ Flatten@ IntegerDigits@ Append[#, k] ], k++]; k]] &, {1, 2}, 80] (* Michael De Vlieger, Dec 14 2019 *)

Crossrefs

Cf. A076990 (3 successive terms have a prime sum), A330424 (3 successive terms AND 3 successive digits have a prime sum).

Sequence in context: A262942 A352808 A076990 * A330424 A057168 A087711

Adjacent sequences: A330431 A330432 A330433 * A330435 A330436 A330437

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Dec 14 2019

Status

approved