A383680 The greater of two consecutive primes whose gap equals the difference between their digital sums.

3, 5, 7, 13, 17, 19, 29, 37, 43, 47, 59, 67, 73, 79, 89, 103, 107, 109, 137, 139, 157, 167, 179, 193, 197, 199, 227, 229, 239, 257, 269, 277, 283, 313, 317, 337, 349, 359, 379, 389, 409, 433, 439, 449, 463, 467, 499, 509, 523, 547, 569, 577, 599, 607, 617, 619

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

19 is a term since 19 - 17 = (1 + 9) - (1 + 7) = 10 - 8 = 2;
23 is not a term since 23 - 19 = 4 != (2 + 3) - (1 + 9) = 5 - 10 = -5.

Mathematica

Select[Prime[Range[120]], #-(pp=NextPrime[#, -1])==DigitSum[#]-DigitSum[pp] &]
Select[Partition[Prime[Range[150]], 2, 1], #[[2]]-#[[1]]==DigitSum[#[[2]]]-DigitSum[#[[1]]]&][[;; , 2]] (* Harvey P. Dale, Jun 08 2026 *)

Crossrefs

Cf. A000040, A001223, A007953, A383679 (lesser), A383681, A383686 (similar with digital roots).

Sequence in context: A046066 A327819 A045398 * A162565 A321363 A355853

Adjacent sequences: A383677 A383678 A383679 * A383681 A383682 A383683

Keyword

nonn,base,easy

Author

Stefano Spezia, May 05 2025

Status

approved