A210629 Each entry is the first of four consecutive primes with equal digital sum.

1442173, 2288509, 2660183, 2805773, 3830891, 4137473, 4951073, 5216137, 5517173, 5521819, 5521891, 5914591, 6474119, 6518173, 7118519, 7570273, 8508473, 8584273, 8689573, 8912591, 9383053, 9958519, 10116373, 10204391, 11418193, 11878873, 11890873, 12948773, 13738163, 13873073, 14377157, 14436391, 14677573, 14732191

Offset

1,1

Comments

The differences between each of the 4-consecutive primes are multiples of 18. - Harvey P. Dale, Jul 22 2016

This sequence consists of primes p = A209396(n) such that A209396(n+1) = nextprime(p+1). Terms such that a(n+1) = nextprime(a(n)+1) give A227931. - M. F. Hasler, May 07 2026

Links

M. F. Hasler, Table of n, a(n) for n = 1..1000, May 07 2026

Example

2288509 is in the sequence because 2288509, 2288527, 2288563, and 2288581 are consecutive primes and the sum of the digits of each equals 34

Mathematica

Transpose[Select[Partition[Prime[Range[1000000]], 4, 1], Total[ IntegerDigits[#[[1]]]]==Total[IntegerDigits[#[[2]]]] == Total[ IntegerDigits[#[[3]]]]==Total[IntegerDigits[#[[4]]]]&]][[1]]
Transpose[Select[Partition[Prime[Range[10^6]], 4, 1], Differences[ Total/@ (IntegerDigits/@#)]=={0, 0, 0}&]][[1]] (* Harvey P. Dale, Jul 22 2016 *)

Prog

(PARI) A210629_first(N) = A395623_row(4, first=N) \\ M. F. Hasler, May 07 2026

Crossrefs

Cf. A071613 (= column 1 of A395623); A066540, A209396, A227931, A227933 (similar for runs of length 2, 3, 5 and 6); A209663 (primes p, p+18 with equal digit sum).

Row 4 of A395623.

Sequence in context: A234657 A015361 A259306 * A156621 A108841 A124490

Adjacent sequences: A210626 A210627 A210628 * A210630 A210631 A210632

Keyword

nonn,base

Author

Harvey P. Dale, Mar 25 2012

Status

approved