A117840 Smaller of two consecutive prime numbers with the same multiplicative digital root.

79, 101, 103, 107, 151, 163, 179, 197, 211, 229, 251, 271, 281, 293, 349, 379, 401, 419, 443, 491, 503, 509, 521, 523, 541, 563, 577, 599, 601, 613, 631, 653, 691, 701, 769, 821, 853, 857, 881, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

79 and 83 are two consecutive primes with the same multiplicative digital root, namely 8.

Mathematica

pod[n_] := Times @@ IntegerDigits[n]; multDigRoot[n_] := NestWhile[pod, n, # > 9 &]; Select[Partition[Select[Range[1000], PrimeQ], 2, 1], Equal @@ multDigRoot /@ # &][[;; , 1]] (* Amiram Eldar, Feb 06 2021 *)
Prime[#]&/@(SequencePosition[NestWhile[Times@@IntegerDigits[#]&, #, #>9&]&/@ Prime[ Range[200]], {x_, x_}][[;; , 1]]) (* Harvey P. Dale, Jan 16 2024 *)

Crossrefs

Cf. A031347, A199975.

Sequence in context: A106757 A285228 A087537 * A296012 A193142 A033250

Adjacent sequences: A117837 A117838 A117839 * A117841 A117842 A117843

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 30 2006

Status

approved