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A127312
Numbers k such that the sum of the digits of k and of k+1 is prime and 2k + 1 is also prime.
0
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
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
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