A209396 Each entry is the first of three consecutive primes with equal digital sum.

22193, 25373, 69539, 107509, 111373, 167917, 200807, 202291, 208591, 217253, 221873, 236573, 238573, 250073, 250307, 274591, 290539, 355573, 373073, 382373, 404273, 407083, 415391, 417383, 439009, 441193, 447907, 515173, 542837, 581873, 582083, 591673

Offset

1,1

Comments

Subsequence of A066540.

The differences between the three primes of the triple are multiples of 18.

This sequence consists of primes p = A066540(k) such that A066540(k+1) = nextprime(p+1). Terms a(n) = precprime(a(n+1)-1) start runs of length 4 and are listed in A210629 = row 4 of A395623. - M. F. Hasler, May 07 2026

Links

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

Example

200807 is in the sequence because 200807, 200843, 200861 are consecutive primes and sum_of_digits(200807)= sum_of_digits(200843)= sum_of_digits(200861)=17

Mathematica

Select[Prime[Range[100000]], Total[IntegerDigits[#]] == Total[IntegerDigits[NextPrime[#, 1]]] == Total[IntegerDigits[NextPrime[#, 2]]] &] (* T. D. Noe, Mar 13 2012 *)
Transpose[Select[Partition[Prime[Range[50000]], 3, 1], Differences[ Total/@ (IntegerDigits/@#)]=={0, 0}&]][[1]] (* Harvey P. Dale, Jul 22 2016 *)

Prog

(PARI) A209396_first(N) = A395623_row(3, first=N) \\ M. F. Hasler, May 07 2026

Crossrefs

Cf. A071613 (= column 1 of A395623); A066540, A210629, A227931, A227933 (similar for runs of length 2, 4, 5 and 6); A209663 (primes p, p+18 with equal digit sum).

Row 3 of A395623.

Sequence in context: A157622 A225392 A225998 * A210295 A060109 A217875

Adjacent sequences: A209393 A209394 A209395 * A209397 A209398 A209399

Keyword

nonn,base

Author

Antonio Roldán, Mar 13 2012

Status

approved