A287308 Primes that can be generated by the concatenation in base 7, in ascending order, of two consecutive integers read in base 10.

17, 41, 401, 601, 701, 751, 1051, 1151, 1201, 1301, 1451, 1601, 1801, 1901, 1951, 2251, 2351, 18233, 19609, 20297, 20641, 21673, 25457, 25801, 26489, 26833, 31649, 33713, 34057, 35089, 36809, 38873, 39217, 41281, 41969, 46441, 47129, 49193, 49537, 51257, 52289

Offset

1,1

Links

Table of n, a(n) for n=1..41.

Example

2 and 3 in base 7 are 2 and 3 and concat(2,3) = 23 in base 10 is 17;
8 and 9 in base 7 are 11 and 12 and concat(11,12) = 1112 in base 10 is 401.

Maple

with(numtheory): P:= proc(q, h) local a, b, c, d, k, n; a:=convert(q+1, base, h); b:=convert(q, base, h); c:=[op(a), op(b)]; d:=0; for k from nops(c) by -1 to 1 do d:=h*d+c[k]; od; if isprime(d) then d; fi; end: seq(P(i, 7), i=1..1000);

Mathematica

With[{b = 7}, Select[Map[FromDigits[Flatten@ IntegerDigits[#, b], b] &, Partition[Range@ 160, 2, 1]], PrimeQ]] (* Michael De Vlieger, May 23 2017 *)

Crossrefs

Cf. A000040, A030458.

Sequence in context: A078847 A201028 A328022 * A355700 A090295 A191457

Adjacent sequences: A287305 A287306 A287307 * A287309 A287310 A287311

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 23 2017

Status

approved