

A175349


a(n) is the smallest positive integer that, when written in binary, contains the binary representations of both the nth prime and the nth composite as (possibly overlapping) substrings.


0



4, 6, 40, 39, 43, 108, 113, 79, 368, 466, 500, 149, 361, 344, 377, 53, 59, 988, 542, 2272, 2121, 1103, 2259, 356, 609, 1253, 3304, 3434, 876, 2929, 4078, 387, 393, 2226, 4787, 1687, 630, 2615, 1336, 5561, 2874, 5820, 382, 4033, 12608, 8391, 13506, 14276, 8931, 14662
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OFFSET

1,1


LINKS



EXAMPLE

The 7th prime is 17, which is 10001 in binary. The 7th composite is 14, which is 1110 in binary. The smallest positive integer that, when written in binary, contains these binary representations as substrings is 113, which is 1110001 in binary. a(7) = 113, therefore.


MATHEMATICA

comp[n_] := FixedPoint[n + 1 + PrimePi[#] &, n + 1 + PrimePi[n]]; sub[n_, x_] := MemberQ[Partition[IntegerDigits[n, 2], IntegerLength[x, 2], 1],
IntegerDigits[x, 2]]; a[n_] := Block[{c = comp[n], p = Prime[n], k}, k = Max[p, c]; While[! sub[k, p]  ! sub[k, c], k++]; k]; Array[a, 50] (* Giovanni Resta, Jul 02 2018 *)


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



