

A070027


Prime numbers whose initial, all intermediate and final iterated sums of digits are primes.


9



2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 83, 101, 113, 131, 137, 151, 173, 191, 223, 227, 241, 263, 281, 311, 313, 317, 331, 353, 401, 421, 443, 461, 599, 601, 641, 797, 821, 887, 911, 977, 1013, 1019, 1031, 1033, 1051, 1091, 1103, 1109, 1123, 1163, 1181, 1213
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OFFSET

0,1


COMMENTS

Subsequence of A046704 ; actually, exactly those numbers for which the orbit under A007953 is a subset of A046704. [From M. F. Hasler, Jun 28 2009]
Supersequences: A046704 is primes p with digit sum s(p) also prime; A207294 is primes p with s(p) and s(s(p)) also prime.
Disjoint sequences: A104213 is primes p with s(p) not prime; A207293 is primes p with s(p) also prime, but not s(s(p)); A213354 is primes p with s(p) and s(s(p)) also prime, but not s(s(s(p))); A213355 is smallest prime p with kfold digit sum s(s(..s(p)).)..)) also prime for all k < n, but not for k = n. Jonathan Sondow, Jun 13 2012


REFERENCES

Glyn Harman, Counting Primes whose Sum of Digits is Prime, Journal of Integer Sequences, Vol. 15 (2012), Article #12.2.2


LINKS

Table of n, a(n) for n=0..52.


EXAMPLE

599 is a term because 599, 5+9+9=23 and 2+3=5 are all prime. 2999 is a term because 2999, 2+9+9+9=29, 2+9=11 and 1+1=2 are all prime. See A062802 and A070026 for related comments.


MAPLE

P:=proc(i) local a, k, n, w; for n from 1 by 1 to i do a:=ithprime(n); while isprime(a) and floor(a/10)>0 do w:=0; k:=a; while k>0 do w:=w+k(trunc(k/10)*10); k:=trunc(k/10); od; a:=w; od; if isprime(a) then print(ithprime(n)); fi; od; end: P(1000);  Paolo P. Lava, Jul 30 2008


MATHEMATICA

dspQ[n_] := TrueQ[Union[PrimeQ[NestWhileList[Plus@@IntegerDigits[#] &, n, # > 9 &]]] == {True}]; Select[Prime[Range[200]], dspQ] (* Alonso del Arte, Aug 17 2011 *)


PROG

(PARI) isA070027(n)={ while(isprime(n), n<9 && return(1); n=vector(#n=eval(Vec(Str(n))), i, 1)*n~)} \\ [From M. F. Hasler, Jun 28 2009]


CROSSREFS

Cf. A070026 (a supersequence), subsequences: A062802, A070028, A070029.
Cf. also A046704, A104213, A207293, A207294, A213354, A213355.
Sequence in context: A046704 A089392 A089695 * A207294 A156658 A118723
Adjacent sequences: A070024 A070025 A070026 * A070028 A070029 A070030


KEYWORD

base,easy,nonn


AUTHOR

Rick L. Shepherd, Apr 14 2002


STATUS

approved



