A366838 Lexicographically earliest sequence of distinct terms > 0 such that any digit d jumping to the right over d digits lands on a prime digit.

1, 2, 3, 4, 5, 6, 7, 8, 20, 22, 23, 25, 27, 9, 21, 32, 10, 24, 12, 26, 33, 11, 35, 28, 37, 13, 29, 15, 52, 14, 53, 55, 57, 30, 72, 31, 73, 34, 75, 36, 38, 77, 39, 50, 51, 222, 223, 220, 221, 224, 225, 226, 227, 228, 229, 230, 54, 56, 16, 58, 59, 70, 71, 232, 233, 74, 231, 235, 76, 78, 17, 79, 202, 237, 203

Offset

1,2

Comments

The prime digits are 2, 3, 5 and 7. This is not a permutation of the natural numbers as 100 and 101 cannot be part of the sequence, for instance.

Links

Table of n, a(n) for n=1..75.

Example

a(5) = 5 jumps over 5 digits and lands on the first 2 of 22, a prime digit;
a(6) = 6 jumps over 6 digits and lands on the 2 of 23, a prime digit;
a(7) = 7 jumps over 7 digits and lands on the 2 of 25, a prime digit;
a(8) = 8 jumps over 8 digits and lands on the 2 of 27, a prime digit;
a(9) = 20: the 2 of 20 jumps over 2 digits and lands on the last 2 of 22, a prime digit;
a(9) = 20: the 0 of 20 jumps over 0 digit and lands on the first 2 of 22, a prime digit; etc.

Mathematica

a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[ar=Array[a, n-1], k]||(vp=Flatten[IntegerDigits/@Join[ar, {k}]];
And@@(PrimeQ@Union@Table[If[IntegerQ[s=vp[[k+1+vp[[k]]]]], s, 2], {k, Length@vp}])
)==False, k++]; k); Array[a, 75]

Crossrefs

Cf. A366943, A366944, A366945, A366946, A366947, A366948, A366949.

Sequence in context: A024650 A037343 A366947 * A236836 A134942 A371260

Adjacent sequences: A366835 A366836 A366837 * A366839 A366840 A366841

Keyword

base,nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Oct 25 2023

Status

approved