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A154780
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Numbers n with d digits such that all digits of n and the last d+1 digits of n^2 are prime.
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1
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5, 35, 235, 335, 2335, 3335, 23335, 32335, 33335, 72335, 233335, 323335, 333335, 372335, 572335, 723335, 2333335, 2372335, 2723335, 3233335, 3323335, 3333335, 3572335, 3723335, 7233335, 7323335, 7372335, 7572335, 22372335, 23333335
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OFFSET
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1,1
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COMMENTS
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Subsequence of A046034; contains A153025 as a subsequence.
Any term with d digits is the concatenation of a prime digit and an earlier term (with d-1 digits).
The sequence is infinite since it contains subsequences b(n) = (10^n-1)/3+2 = (5,35,335,3335,..), c(n) = 23*10^n+b(n) = (235,2335,23335,...), d(n) = 3233*10^n+b(n), e(n) = 7233*10^n+b(n) etc.
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LINKS
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Table of n, a(n) for n=1..30.
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FORMULA
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For all n, a(n) = 5 mod 10. For a(n)>5, a(n)=35 mod 100. For a(n)>35, a(n)=235 or 335 mod 1000. For a(n)>335, a(n)=2335 or 3335 mod 10^4.
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MATHEMATICA
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Select[Range[5, 24000000, 5], And@@PrimeQ[IntegerDigits[#]]&& And@@ PrimeQ[ Take[ IntegerDigits[#^2], -(IntegerLength[#]+1)]]&] (* Harvey P. Dale, Dec 31 2012 *)
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PROG
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(PARI) last=[0]; {for( d=1, 8, new=[]; forprime( p=0, 9, for( k=1, #last, is_A046034((p*10^(d-1)+last[k])^2%10^(d+1)+20*10^d) & new=concat( new, p*10^(d-1)+last[k]))); print1(last=new, ", "))} /*for slightly more efficient code see A154779 */
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CROSSREFS
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Sequence in context: A002074 A187444 A166176 * A007995 A091928 A155127
Adjacent sequences: A154777 A154778 A154779 * A154781 A154782 A154783
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KEYWORD
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base,easy,nice,nonn
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AUTHOR
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M. F. Hasler, Jan 23 2009
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STATUS
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approved
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