A106711 - OEIS

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A106711

Smaller prime of the set of two consecutive primes each of whose sum of digits is prime.

2, 3, 5, 7, 23, 41, 43, 61, 83, 131, 137, 151, 173, 191, 193, 197, 223, 227, 263, 281, 311, 313, 317, 331, 353, 373, 397, 401, 443, 461, 463, 571, 593, 599, 601, 641, 643, 733, 751, 797, 821, 823, 827, 881, 883, 911, 971, 1013, 1031, 1033, 1091, 1093, 1097, 1103

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

a(5)=23 is a term because it is the first of two consecutive primes (23 and 29), each of which has a prime sum of digits: 2 + 3 = 5 and 2 + 9 = 11.

MATHEMATICA

Select[Partition[Prime[Range[200]], 2, 1], PrimeQ[Total[IntegerDigits[ #[[1]]]]] && PrimeQ[Total[IntegerDigits[#[[2]]]]]&][[All, 1]] (* or *) Prime[#]&/@SequencePosition[Table[If[PrimeQ[Total[IntegerDigits[n]]], 1, 0], {n, Prime[Range[200]]}], {1, 1}][[All, 1]] (* The second program requires Mathematica version 10 or later, but is more efficient because it only requires testing each prime for its sum of digits once. *) (* Harvey P. Dale, Jul 27 2017 *)

Prime@Select[Range[500], PrimeQ[Total[IntegerDigits[Prime[#]]]] && PrimeQ[Total[IntegerDigits[Prime[# + 1]]]] &] (* César Eliud Lozada, Mar 31 2024 *)

CROSSREFS

Sequence in context: A210566 A155873 A362678 * A235110 A048398 A059170

Adjacent sequences: A106708 A106709 A106710 * A106712 A106713 A106714

KEYWORD

base,nonn

AUTHOR

Shyam Sunder Gupta, May 14 2005

EXTENSIONS

Definition clarified by Harvey P. Dale, Jul 27 2017

STATUS

approved