A383686 The greater of two consecutive primes whose gap equals the difference between their digital roots.

3, 5, 7, 13, 17, 23, 31, 41, 43, 53, 61, 71, 79, 89, 103, 107, 113, 131, 139, 151, 167, 179, 193, 197, 229, 233, 241, 269, 277, 283, 311, 313, 349, 359, 383, 401, 421, 439, 449, 463, 467, 491, 503, 547, 571, 593, 601, 617, 619, 643, 647, 661, 683, 743, 761, 773

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Example

127 is not a term since 127 - 113 = 14 = A010888(127) - A010888(113) = 1 - 5 = -4;
131 is a term since 131 - 127 = 4 = A010888(131) - A010888(127) = 5 - 1.

Mathematica

A010888[n_]:=n - 9*Floor[(n-1)/9]; Select[Prime[Range[150]], #-(pp=NextPrime[#, -1])==A010888[#]-A010888[pp] &]

Crossrefs

Cf. A000040, A001223, A010888, A383680 (similar with digital sums), A383685 (lesser), A383687.

Sequence in context: A028879 A067567 A104294 * A372141 A262100 A171566

Adjacent sequences: A383683 A383684 A383685 * A383687 A383688 A383689

Keyword

nonn,base,easy

Author

Stefano Spezia, May 05 2025

Status

approved