A127312 Numbers k such that the sum of the digits of k and of k+1 is prime and 2k + 1 is also prime.

1, 2, 3, 5, 6, 8, 11, 14, 15, 18, 20, 21, 23, 26, 30, 33, 35, 36, 41, 44, 50, 51, 53, 54, 56, 63, 65, 68, 74, 78, 81, 83, 86, 90, 95, 96, 99, 105, 111, 113, 114, 116, 120, 125, 128, 131, 134, 135, 140, 141, 146, 153, 155, 158, 168, 173, 176, 186, 191, 194, 198, 200

Offset

1,2

Links

Table of n, a(n) for n=1..62.

Example

Sum of the digits of 21 and 22 is 2+1+2+2 = 7 and 21+22 = 43. Both 7 and 43 are prime, hence 21 is a term.

Maple

sod:=proc(n) local b: b:=n->convert(n, base, 10): sum(b(n)[j], j=1..nops(b(n))) end: a:=proc(n) if isprime(2*n+1) and isprime(sod(n)+sod(n+1)) then n fi end: seq(a(n), n=1..280); # Emeric Deutsch, Apr 01 2007

Mathematica

Select[Range[300], And@@PrimeQ[{2#+1, Total[IntegerDigits[#]]+ Total[ IntegerDigits[#+1]]}]&] (* Harvey P. Dale, May 20 2012 *)

Prog

(Magma) [ n: n in [1..200] | IsPrime(&+Intseq(n, 10) + &+Intseq(n+1, 10)) and IsPrime(2*n+1) ]; /* Klaus Brockhaus, Apr 06 2007 */

Crossrefs

Sequence in context: A266542 A095172 A179101 * A081830 A238006 A329289

Adjacent sequences: A127309 A127310 A127311 * A127313 A127314 A127315

Keyword

nonn,base

Author

J. M. Bergot, Mar 28 2007

Extensions

Edited and extended by Emeric Deutsch and Klaus Brockhaus, Apr 01 2007

Status

approved