A092595 Numbers k such that the sum of decimal digits of k and k+1 are both prime numbers, i.e., both k and k+1 are in A028834.

2, 11, 20, 29, 49, 101, 110, 119, 139, 199, 200, 209, 229, 289, 319, 379, 409, 469, 559, 649, 739, 829, 919, 1001, 1010, 1019, 1039, 1099, 1100, 1109, 1129, 1189, 1219, 1279, 1309, 1369, 1459, 1549, 1639, 1729, 1819, 1909, 2000, 2009, 2029, 2089, 2119, 2179

Offset: 1

Author

Labos Elemer, Mar 17 2004

Keywords

• base
• nonn

Comments

Interestingly, the following numbers n are such that the sum of the decimal digits of n, n+1, and n+2 are all prime numbers: 199, 1099, 10099, 19999, 100099, 109999, . . . -Harvey P. Dale, Jan 28 2025

Examples

			For k=4429, digitsum(k) = 4 + 4 + 2 + 9 = 19, digitsum(k+1) = 4 + 4 + 3 + 0 = 11.
		

Links

• J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..10000.

Crossrefs

Cf. A028834.

Programs

Mathematica

t=Table[0, {256}]; j=1; Do[s=Apply[Plus, IntegerDigits[n]]; s1=Apply[Plus, IntegerDigits[n+1]]; If[PrimeQ[s]&&PrimeQ[s1], Print[n]; t[[j]]=n; j=j+1], {n, 1, 10000}]; t
DeleteCases[ParallelTable[If[PrimeQ[Total[IntegerDigits[n]]]&&PrimeQ[Total[IntegerDigits[n+1]]],n,a],{n,2,952999}],a] (* J.W.L. (Jan) Eerland, Dec 20 2021 *)
SequencePosition[Table[If[PrimeQ[Total[IntegerDigits[n]]],1,0],{n,2500}],{1,1}][[;;,1]] (* Harvey P. Dale, Jan 28 2025 *)

PARI

isok(n) = isprime(sumdigits(n)) && isprime(sumdigits(n+1)); \\ Michel Marcus, Jul 29 2017