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A154780 Numbers n with d digits such that all digits of n and the last d+1 digits of n^2 are prime. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..30.

FORMULA

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.

MATHEMATICA

Select[Range[5, 24000000, 5], And@@PrimeQ[IntegerDigits[#]]&& And@@ PrimeQ[ Take[ IntegerDigits[#^2], -(IntegerLength[#]+1)]]&] (* Harvey P. Dale, Dec 31 2012 *)

PROG

(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 */

CROSSREFS

Sequence in context: A002074 A187444 A166176 * A007995 A091928 A305739

Adjacent sequences:  A154777 A154778 A154779 * A154781 A154782 A154783

KEYWORD

base,easy,nice,nonn

AUTHOR

M. F. Hasler, Jan 23 2009

STATUS

approved

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Last modified June 7 02:48 EDT 2020. Contains 334836 sequences. (Running on oeis4.)